**NCERT Exemplar Class 8 Maths Chapter 9 Comparing Quantities**

**Multiple Choice Questions**

**Question. 1 Suppose for the principal P, rate R% and time T, the simple interest is S and compound interest is C. Consider the possibilities**

**(i) C>S**

**(ii) C = S**

**(iii) C <S Then,**

**(a) only (i) is correct (b) either (i) or (ii) is correct**

**(c) either (ii) or (iii) is correct (d) only (iii) is correct**

**Solution.** (a) Let the principal (P) = Rs. 100

Rate of interest (R) = 100% and time period (T) = 2 yr

**Question. 2 Suppose a certain sum doubles in 2 yr at r% rate of simple interest per annum and R°/o rate of interest per annum compounded annually. Then,**

**(a) r < R (b) R<r**

**(c)R = r (d) Cannot be determined**

**Solution.** (b) If the total amount received after 2 yr is same for both simple interest and compound interest on same principal, then the rate of simple interest is greater than the rate of compound interest.

i.e.R<r

Hence, option (b) is correct.

**Question. 3 The compound interest on Rs. 50000 at 4% per annum for 2 yr compounded annually is ****(a) Rs. 4000 (b) Rs. 4080 (c) Rs. 4280 (d) Rs. 4050**

**Solution.** (b) Given, principal (P) = Rs. 50000

Rate of interest (R%) = 4% per annum

Time period (T) = 2 yr We know that,

**Question. 4 If marked price of an article is Rs. 1200 and the discount is 12%, then the selling price of the article is ****(a)Rs. 1056 (b) Rs. 1344 (c) Rs. 1212 (d)Rs.1188**

**Solution.** (a) Given, marked price of an article = Rs. 1200 Discount % = 12%

Discount = Discount % on marked price

= A x 1200=12 x 12 = Rs.144

Selling price = Marked price – Discount Selling price = Rs.11200 – Rs. 144 = Rs.1056 Hence, option (a) is correct.

**Question. 5 If 90% of x is 315 km, then the value of x is**

**(a) 325 km (b) 350 km (c) 350 m**

**Solution.** (b) We have, 90% of x = 315 km

**Question. 6 To gain 25% after allowing a discount of 10%, the shopkeeper must mark the price of the article which cost him Rs. 360 as**

**(a) Rs. 500 (b) Rs. 450 (c) Rs. 460 (d) Rs. 486**

**Solution**. (a) Let the marked price of the article be Rs.x.

Cost price of the article = Rs. 360 According to the question,

**Question. 7 If a% is the discount per cent on marked price x, then discount is**

**(a)\(\frac { x }{ a } \)x 100 (b) \(\frac { a }{ x } \) x 100**

**(c) x x \(\frac { a }{ 100 } \) (d)\(\frac { 100 }{ xa } \)**

**Solution.** (c) Since, discount can be calculated always on marked price, when discount percentage is given. Discount = Discount % on marked price = \(\frac { a }{ 100 } \)x x

Hence, option (c) is correct.

**Question. 8 Ashima took a loan of Rs. 100000 at 12% per annum compounded half-yearly. She paid Rs. 112360. If (1.06)2 is equal to 1.1236, then the period for which she took the loan is**

**(a) 2 yr (b) 1 yr**

**(c) 6 months (d) 1 \(\frac { 1 }{ 2 } \) yr**

**Solution.** (b) Given, principal (P) = Rs.100000

Rate of interest (R%) = 12% per annum compounded half-yearly Let m be the time period, v Amount paid = Rs.112360

**Question. 9 For calculation of interest compounded half-yearly, keeping the principal same, which one of the following is true?**

**(a) Double the given annual rate and half the given number of years**

**(b) Double the given annual rate as well as the given number of years**

**(c) Half the given annual rate as well as the given number of years**

**(d) Half the given annual rate and double the given number of years**

**Solution.** (d)If interest is compounded half-yearly, then R=\(\frac { R }{ 2 } \) and T=2T=2n

So, half the given annual rate and double the given number of years. Hence, option (d) is correct.

**Question. 10 Shyama purchases a scooter costing Rs. 36450 and the rate of sales tax is 9%, then the total amount paid by her is**

**(a) Rs. 36490.50 (b) Rs. 39730.50**

**(c) Rs. 36454.50 (d) Rs. 33169.50**

**Solution.** (b) Since, sales tax is charged on the sale of an item by the government and is added to the bill amount. Shyama purchase a scooter of costing = Rs. 36450 Sales tax paid =9%

So, total amount paid by her

= Rs. 36450 of 9%+ Rs. 36450

= \(\frac { 9 }{ 100 } \)x36450 + 36450

= 9 x 364.5 + 36450 = 3280.5 + 36450 = Rs. 39730.5

Hence, option (b) is correct.

**Question. 11 The marked price of an article is Rs. 80 and it is sold at Rs. 76, then the discount rate is**

**(a) 5% (b) 95%**

**(c) 10% (d) approx 11 %**

**Solution.** (a) The marked price of an article = Rs. 80 Sold price of the article = Rs. 76 We know that,

Selling price = Marked price – Discount Discount = Marked price – Selling price

=> Discount = Rs.80-Rs.76 = Rs.4

Discount % = \(\frac { 4 }{ 80 } \) x 100= \(\frac { 40 }{ 80 } \) = 5%

Hence, option (a) is correct.

**Question. 12 A bought a tape recorder for Rs. 8000 and sold it to B. B in turn sold it to C, each earning a profit of 20%. Which of the following is true?**

**(a) A and B earn the same profit (b) A earns more profit than B**

**(c) A earns less profit than<5 (d) Cannot be determined**

**Solution.** (c) Cost price of tape recorder for/4 = Rs.8000

Cost price of tape recorder for B =20% profit on cost price for A

=\(\frac { 20 }{ 100 } \) x 8000 + 8000

=20 x 80 + 8000

=1600 + 8000=Rs.9600

Cost price of tape recorder for C=20% profit on cost price for B

=\(\frac { 20 }{ 100 } \) x 9600 + 9600

=1929 + 9600=Rs.11520

Here, profit for A= Rs.1600 Profit for B = Rs.1920

So, A earns less profit than B.

Hence, option (c) is correct.

**Question. 13 Latika bought a teapot for Rs. 120 and a set of cups for Rs. 400. She sold teapot at a profit of 5% and cups at a loss of 5%. The amount received by her is**

**(a) Rs. 494 (b) 7 546**

**(c) Rs. 506 (d) Rs. 534**

**Solution.** (c) Latika bought a teapot = Rs. 120 and a set of cups = Rs. 400 She sold teapot at a profit of 5%, So, selling price of teapot =\(\frac { 5 }{ 100 } \) x 120 + 120

= \(\frac { 120 }{ 20 } \) +120

= 6 + 120 = Rs.126 Also, she sold cups at a loss of 5%.

So, selling price of cups = 400 –\(\frac { 5 }{ 100 } \) x 400

= 400 – 20 = Rs. 380

Then, the total amount received by her = Rs. 126 + Rs. 380 = Rs. 506 Hence, option (c) is correct.

**Question. 14 A jacket was sold for Rs. 1120 after allowing a discount of 20%. The marked price of the jacket is**

**(a) Rs. 1440 (b) Rs. 1400 (c) Rs. 960 (d) Rs. 866.66**

**Solution.** (b) Let the marked price of the jacket be Rs. x.

Discount % on marked price = 20%

**Question. 15 A sum is taken for two years at 16% per annum. If interest is .compounded after every three months, the number of times for which interest is charged in 2 yrs is**

**(a) 8 (b) 4 (c) 6 (d) 9**

**Solution.** (a) Since, rate of interest is calculated after every three months. Similarly, the time period for amount in a year will 4 times.

If amount is taken for 2 yr, means 4×2 = 8 times charged in 2 yr.

Hertee, option (a) is correct.

**Question. 16 The original price of a washing machine which was bought for Rs. 13500 including of 8% VAT, is**

**(a) Rs. 12420 (b) Rs. 14580 (c) Rs.12500 (d) Rs. 13492**

**Solution.** (a) The price of the washing machine = Rs.13500

VAT [Value Added Tax] is included in selling price, which is 8%.

The original price of the washing machine including of 8% VAT

= 13500-13500 x \(\frac { 8 }{ 100 } \)

= 13500-135 x 8 = 13500-1080= Rs.12420 Hence, option (a) is correct.

**Question. 17 Avinash bought an electric iron for Rs. 900 and sold it at a gain of 10%. He sold another electric iron at 5% loss which was bought**

**Rs. 1200. On the transaction, he has a**

**(a) profit of Rs. 75 (b) loss of Rs. 75 (c) profit of Rs. 30 (d) loss of Rs. 30**

**Solution.** (c) Avinash bought an electric iron = Rs. 900 He sold it, at 10% profit.

So, selling price of the electric iron = \(\frac { 10 }{ 100 } \)x 900 + 900

= 90+ 900 = Rs. 990

He also sold another electric iron at 5% loss.

Cost price of another electric iron = Rs.1200

So, selling price of the electric iron = 1200\(\frac { 5 }{ 100 } \) x 1200

= 1200-60 = Rs.1140

Total amount paid by Avinash for purchasing electric irons = Rs. 900 + Rs.1200 = Rs.2100 Total received amount = Rs. 990 + Rs. 1140

= Rs. 2130 So, his profit = Rs.2130- Rs.2100 = Rs.30in transaction.

Hence, option (c) is correct.

**Question. 18 A TV set was bought for t 26250 including 5% VAT. The original price of the TV set is**

**(a) Rs. 27562.50 (b) Rs. 25000 (c) Rs. 24937.50 (d) Rs. 26245**

**Solution.** (c) Cost price of TV set = Rs. 26250.

VAT including = 5%

Original price = Cost price of article including VAT = 26250 \(\frac { 5 }{ 100 } \) x 26250

= 26250-\(\frac { 26250 }{ 20 } \)

= 26250-1312.5

So, original price of the TV set = Rs. 24937.5 Hence, option (c) is correct.

**Question. 19 40% of [100 – 20% of 300] is equal to**

**(a) 20 (b) 16 (c) 140 (d) 64**

**Solution**. (b) 40% of [100-20% of 300]

Hence, option (b) is correct.

**Question. 20 Radhika bought a car for Rs. 250000. Next year, its price decreased by 10% and further next year, it decreased by 12%. In the two years, overall decrease per cent in the price of the car is**

**(a) 3.2% (b) 22% (c) 20.8% (d) 8%**

**Solution.** (c) Radhika bought a car for Rs. 250000.

Cost price of a car = Rs.250000

Its price decreased next year for 10%.

Hence, option (c) is correct.

**Fill in the Blanks**

**In questions 21 to 45, fill in the blanks to make the statements true.**

**Question. 21 ……………. is a reduction on the marked price of the article.**

**Solution.** Discount is a reduction on the marked price of the article.

**Question. 22 Increase of a number from 150 to 162 is equal to increase of ………………..per cent.**

**Solution**. Initial number = 150

Final number = 162

Increased number = 162 -150 = 12

Per cent of increased number = \(\frac { 12 }{ 150 } \) x 100 =\(\frac { 120 }{ 15 } \) = 8%

**Question. 23 15% increase in price of an article, which is Rs. 1620, is the increase of ?**

**Solution**. Let the price of the article be Rs. x.

**Question. 24 Discount =…………….**

**Solution.** Discount = MP – SP

Here, MP = Marked price, and SP = Selling price

**Question. 25 Discount = Discount % of ……………**

**Solution.** Discount = Discount % of marked price

[ discount is a reduction given on marked price]

**Question. 26 ………………….is charged on the sale of an item by the government and is added to the bill amount.**

**Solution.** Sales tax is charged on the sale of an item by the government and is added to the bill amount.

Sales tax = Tax % of bill amount

**Question. 27 Amount when interest is compounded annually, is given by the formula……………….**

**Solution.** Amount when interest is compounded annually, is given by the formula

where, P = principal, R = rate per annum and T = time

**Question. 28 Sales tax = Tax% of……………….**

**Solution**. Sales tax=Tax % of bill amount

**Question. 29 The time period after which the interest is added each time to form a new principal, is called the ……………**

**Solution.** The time period after which the interest is added each time to form a new principal, is called the conversion period.

**Question. 30 ……………… expenses are the additional expenses incurred by a buyer for an item over and above its cost of purchase.**

**Solution.** Overhead expenses are the additional expenses incurred by a buyer for an item over and above its cost of purchase.

**Question. 31 The discount on an item for sale is calculated on the ……………..**

**Solution.** The discount on an item for sale is calculated on the marked price.

**Question. 32 When principal P is compounded semi-annually at r% per annum for t years, then amount = ……………..**

**Solution.** When principal P is compounded semi-annually at r% per annum for t years.

**Question. 33 Percentages are to fractions with ………………. equal to 100.**

**Solution.** Percentages are equal to fractions with denominator equal to 100.

e.g. 8% means \(\frac { 8 }{ 100 } \)

**Question. 34 The marked price of an article when it is sold for ? 880 after a discount of 12%, is ……………..**

**Solution.** Selling price of an article = Rs.880 Discount % = 12%

We know that, discount is calculated oh marked price. Let the marked price be Rs. x.

**Question. 35 The compound interest on Rs. 8000 for one year at 16% per annum compounded half-yearly is …………… , given that ****\({ 1.08 }^{ 2 }\) = 1.1664.**

**Solution.** Given, principal(P) = Rs.8000

Time period (7) = 1 yr

Rate (ft) = 16% per annum compounded half-yearly

**Question. 36 In the first year on an investment of Rs. 600000, the loss is 5% and in the second year, the gain is 10%, the net result is ……………….**

**Solution.** Investment amount = 7600000

In 1st year, the loss in 1st year = 5%.

So, investment in 1st year = 600000 – \(\frac { 5 }{ 100 } \) x 600000= 600000 – 30000 = 7 570000

In llnd year, the gain is 10%.

So, net investment = 570000 +\(\frac { 10 }{ 100 } \) x 570000= 570000 + 57000 = 7627000

**Question. 37 If amount on the principal of Rs. 6000 is written as 6000 \({ \left[ 1+\frac { 5 }{ 100 } \right] }^{ 3 }\)and compound interest payable half-yearly, then rate of interest per annum is…………….. and……………… time (in years) is**

**Solution.** If amount on the principal of 7 6000 is written as 6000\({ \left[ 1+\frac { 5 }{ 100 } \right] }^{ 3 }\) of and compound interest

payable half-yearly, then rate of interest per annum is 10% and time (in years) is 1\(\frac { 1 }{ 2 } \) yr.

**Question. 38 By selling an article for Rs. 112000, a girl gains 40%. The cost price of the article was ……………..**

**Solution.** Selling price of an article = 7 112000

Gain% = 40% .

**Question. 39 The loss per cent on selling 140 geometry boxes at the loss of SP of 10 geometry boxes is equal to ………………..**

**Solution.** Let the selling price of 1 geometry box be Rs. 1.

So, the selling price for 140 geometry boxes = Rs.1 x 140 = Rs.140

Similarly, selling price of 10 geometry boxes = Rs. 1 x 10 = Rs. 10 v

Loss = Selling price of 10 geometry boxes = Rs.10

**Question. 40 The cost price of 10 tables is equal to the sale price of 5 tables. The profit per cent in this transaction is ……………..**

**Solution.** Let the cost price of 1 table be Rs. 1.

The cost price of 10 tables = Sale price of 5 tables Profit = Cost price of 5 tables = Rs. 5

Profit percentage =\(\frac { profit }{ CP } \) x 100 = \(\frac { 5 }{ 5 } \)x 100 = 100%

**Question. 41 Abida bought 100 pens at the rate of Rs. 3.50 per pen and pays a sales tax of 4%. The total amount paid by Abida is .**

**Solution.** Number of pens bought by Abida = 100 Rate of per pen = Rs.3.50 So, cost of 100 pens = 100 x 3.50 = 1350 Abida also paid 4% sales tax on Rs. 350.

So, the total amount paid by Abida = 350x \(\frac { 4 }{ 100 } \) + 350= 350 x \(\frac { 1 }{ 25 } \) + 350= 14+ 350

= Rs. 364 .

**Question. 42 The cost of a tape recorder is Rs. 10800 inclusive of sales tax charged at 8%. The price of the tape recorder before sales tax was charged, is ……………….**

**Solution.** The cost of tape recorder, inclusive of 8% sales tax = Rs.10800 Let the price of the tape recorder before sales tax be Rs. x.

**Question. 43 2500 is greater than 500 by …………..%.**

**Solution.** Difference between 2500 and 500 = 2500 – 500 = 2000

Hence, \(\frac { 2000 }{ 500 } \) x 100 = \(\frac { 2000 }{ 5 } \) = 400%

**Question. 44 Four times a number is a …………….% increase in the number.**

**Solution.** Let x be the number.

So, four times of x is Ax.

Hence, Ax is greater than x by 4x – x = 3x

Percentage increase in x = \(\frac { 3x }{ x } \) x 100 = 300%

**Question. 45 5% sales tax is charged on an article marked X 200 after allowing a discount of 5%, then the amount payable is …………….**

**Solution.** The marked price of the article = 1200 Discount = 5%

Selling price of the article = 200 – \(\frac { 5 }{ 100 } \) x 200

=200 -10 = Rs.190

Selling price including 5% sales tax = 190 + \(\frac { 5 }{ 100 } \) x 190

= 190+ 9.5 = Rs.199.5

Payable amount = Rs. 199.50

**True/False**

**Inquestions 46 to 65, state whether the statements are True or False.**

**Question. 46.Tp calculate the growth of a bacteria if the rate of growth is known, the formula for calculatiorfof amount in compound interest can be used.**

**Solution.** True

For calculating the growth of a bacteria4f the rate of growth is known, then we can use the formula for calculation of amount in compound interest.where, A = growth after nyears, P = initial number of bacteria and R = rate of growth

**Question. 47 Additional expenses made after buying an article are included in the cost price and are known as Value Added Tax.**

**Solution.** False

In the selling price (known as MRP) include the tax known as VAT (Value Added Tax).

Hence, VAT is always included in selling price.

**Question. 48 Discount is a reduction given on cost price of an article.**

**Solution.** False

Discount is a reduction given on marked price not on cost price.

**Question. 49 Compound interest is the interest calculated on the previous year’s amount.**

**Solution.** True

v Compound interest, Cl = A – P

where,

\({ A=P\left[ 1+\frac { R }{ 100 } \right] }^{ n }\)

Here, P = Principal on previous year’s amount and A = Present year’s amount R = Rate of interest and n = Time

**Question. 50 CP = MP – Discount**

**Solution.** False

The relation between marked price and discount is given by Selling price = Marked price – Discount

**Question. 51 A man purchased a bicycle for Rs. 1040 and sold it for Rs. 800. His loss per cent is 30%.**

**Solution.** False

Cost pride of the bicycle = Rs. 1040 Selling price of the bicycle =Rs. 800

Loss = Cost price – Selling price = Rs.1040 -Rs.800 = Rs.240

**Question. 52 Three times a number is 200% increase in the number, then one-third of the same number is 200% decrease in the number.**

**Solution.** False

Let x be the number.

So, three times of x = 3x

Difference between 3x and x=3x-x=2x

**Question. 53 Simple interest on a given amount is always less than or equal to the compound interest on the same amount for the same time period and at the same rate of interest per annum.**

**Solution.** False

For 1 yr, the simple interest and compound interest for same amount on same rate of interest are equal.

But for 2 yr, the simple interest is less than the compound interest for same amount on same rate of interest.

**Question. 54 The cost of a sewing machine is Rs. 7000. Its value depreciates at 8% per annum. Then, the value of the machine after 2 yr is Rs. 5924.80.**

**Solution.** True

Principal = Rs.7000

Rate of depreciation = 3% per annum Time period = 2 yr

**Question. 55 If the discount of Rs. y is available on the marked price of Rs. x, then the discount per cent is\(\frac { x }{ y }\) x 100%,**

**Solution.** False

Marked price =Rs.x

Discount amount =Rs.y

**Question. 56 Number of students appearing for class X CBSE examination increases from 91422 in 1999-2000 to 116054 in 2008-09. Increase in the number of students appeared is approximately 27%.**

**Solution.** True

Number of students increase from 116054 in 2008-09 to 91422 in 1999-2000

= 116054 – 91422 = 24632

Percentage of increase in number of students

**Question. 57.Selling price of 9 articles is equals to the cost price of 15 articles .In this transaction the profit of 66\(\frac { 2 }{ 3 }\)%**

**Solution.** True

**Question. 58The compound interest on a sum of Rs. P for T years at R% per annum compounded annually is given by the formula,****\(P\left[ 1+\frac { R }{ 100 } \right] \)**

**Solution.** False

**Question. 59 In case of gain, SP =\(\frac { (100+gain%)\times CP }{ 100 } \)**

**Solution.** True

**Question. 60 In case of loss, CP =\(\frac { 100\times SP }{ 100+Loss% } \)**

**Solution.** False

**Question. 61 The value of a car, bought for Rs. 440000 depreciates each year by 10% of its value at the beginning of that year. So, its value becomes Rs. 308000 after three years.**

**Solution.** False

The value of a car i.e. principal = Rs.440000 Rate of depreciation (R%) = 10% per annum Time period (T) = 3 yr

**Question. 62 The cost of a book marked at Rs. 190 after paying a sales tax of 2% is Rs. 192.**

**Solution.** False

Marked price of a book = Rs.190 .

**Question. 63 The buying price of 5 kg of flour with the rate Rs. 20 per kg, when 5% sates tax is added on the purchase, is ****Rs. 21.**

**Solution.** True

Total flour bought = 5 kg

Rate of one kg flour = Rs.20

**Question. 64 The original price of a shampoo bottle bought for Rs. 324, if 8% VAT is included in the price, is Rs. 300.**

**Solution.** False

The original price of a shampoo bottle = Rs.300

Cost price of shampoo bottle after 8% VAT

**Question. 65 Sales tax is always calculated on the cost price of an item and is added to the value of the bill.**

**Solution.** False

Sales tax is always calculated on the selling price of an item and is added to the value of the bill.

**Question. 66 In a factory, women are 35% of all the workers, the rest of the workers being men. The number of men exceeds that of women by 252. Find the total number of workers in the factory.**

**Solution.** Percentage of women in factory = 35%

Percentage of men in factory = 100 – 35 = 65%

Let the number of persons in the factory be x.

According to the question,

**Question. 67 Three bags contain 64.2 kg of sugar. The second bag contains \(\frac { 4 }{ 5 }\) of the contents of the first and the third contains 45 \(\frac { 1 }{ 2 }\) % of what there is in the second bag. How much sugar is there in each bag?**

**Solution.** The total weight of sugar in three bags = 64.2 kg Let the first bag contains x kg sugar.

**Question. 68 Find the SP, if**

**(a) MP = Rs. 5450 and discount = 5%**

**(b) MP = Rs.1300 and discount = 15%**

**Solution.** (a) Marked price = 7 5450 Discount % = 5%

**Question. 69 Find the MP, if**

**(a) SP = Rs. 495 and discount = 1%**

**(b) SP = Rs. 9250 and discount = 7\(\frac { 1 }{ 2 }\) %**

**Solution.** (a) Selling price (SP) = 7495 Discount % = 1%

**Question. 70 Find discount in percent when**

**(a) MP = Rs.625 and SP = Rs.562.50**

**(b) MP = Rs.900 and SP = Rs.873**

**Solution.** (a) Marked price (MP) = Rs.625 Selling price (SP) = Rs. 562.50

**Question. 71 The marked price of an article is Rs. 500. The shopkeeper gives a discount of 5% and still makes a profit of 25%. Find the cost price of the article.**

**Solution.** Given, marked price of an article = Rs.500 Discount % = 5%

But it makes a profit of 25%.

Let the cost price of the article be Rs. x.

**Question. 72 In 2007-08, the number of students appeared for Class X examination was 105332 and in 2008-09 the number was 116054. If 88151 students pass the examination in 2007-08 and 103804 students in 2008-09. What is the increase or decrease in pass percentage in class X result?**

**Solution.** Number of students appeared in 2007-08 = 105332 Number of students appeared in 2008-09 = 116054 Number of students passed in 2007-08 = 88151 Number of students passed in 2008-09 = 103804

**Question. 73 A watch worth Rs. 5400 x is offered for sale at Rs. 4500. What per cent discount is offered during the sale?**

**Solution.** Marked price of a watch = Rs.5400

Selling price = Rs.4500

Discount = Marked price – Selling price = Rs.5400 – Rs.4500 = Rs.900

**Question. 74 In the year 2001, tbe number of malaria patients admitted in the hospitals of a state was 4375. Every year this number decreases by 8%. Find the number of-patients in 2003.**

**Solution.** The number of malaria patients admitted in a hospital in 2001 = 4375 Rate of decrement of malaria patients = 8%

Time period = 2 yr i.e.2003-2001=2 yr

Let the number of patients in 2003 be A.

**Question. 75 Jyotsana bought a product for Rs. 3155 including 4.5% sales tax. Find the price before tax was added.**

**Solution.** A product bought by Jyotsana for Rs. 3155 including 4,5% sales tax.

Let the price of the product before sales tax be Rs. x.

**Question. 76 An average Urban Indian uses about 150 L of water everyday.**

**(a) What per cent of water is used for bathing and sanitation together per day?**

**(b) How much less per cent of water is used for cooking in comparison to that used for bathing?**

**(c) What per cent of water- is used fdr drinking, cooking and gardening together?**

**Solution.** (a) On the basis of given details, water used for bathing per day = 20 L

Water used for sanitation = 40 L

Total water used per day = 150 L

**Question. 77 In 1975, the consumption of water for human use was about 3850 cu km/yr. It increased to about 6000 cu km/yr in the year 2000.**

**Find the per cent increase in the consumption of water from 1975 to 2000. Also, find the annual per cent increase in consumption**

**(assuming water consumption increases uniformly).**

**Solution.** The consumption of water for human in 1975 = 3850 cu km/yr

The consumption of water for human in 2000 = 6000 cu km/yr

Increase in consumption of wgjer in 1975 to 2000 = 6000 – 3850 = 2150 cu km/yr

**Question. 78 Harshna gave her car for service at service station on 27-05-2009 and was charged as follows**

**(a)3.10 L engine oil @ Rs. 178.75 per litre and VAT @ 20%.**

**(b)Rs. 1105.12 for all other services and VAT @ 12.5%.**

**(c)Rs. 2095.80 as labour charges and service tax @ 10%.**

**(d)3% cess on service tax.**

**Find the bill amount.**

**Solution.** (a) The total litres of engine oil used = 3.10 L

Rate of engine oil per litres =Rs. 178.75

The cost of engine oil = 3.10 x 17875= Rs. 554.125

**Question. 79 Given, the principal = Rs.40000, rate of interest = 8% per annum compound annually. Find**

**(a) Interest if period is one year.**

**(b) Principal for Ilnd year.**

**(c) Interest for Ilnd year.**

**(dj Amount if period is ttoo year.**

**Solution.** Given, principal (P)= Rs.40000

Rate of interest (R) = 8% per annum

**Question. 80 In Delhi University, in the year 2009-10, 49000 seats were available for admission to various courses at graduation level. Out of these 28200 seats were for the students of General Category while 7400 seats were reserved for SC and 3700 seats for ST. Find the percentage of seats available for**

**(a) students of General Category.**

**(b) students of SC Category and ST Category taken together.**

**Solution.** The total number of seats available for admission in 2009-10 = 49000

Seats reserved for General Category students = 28200

Seats reserved for SC Category students = 7400

Seats reserved for ST Category students = 3700

**Question. 81 Prachi bought medicines from a medical store as prescribed by her doctor for Rs 36.40 including 4% VAT. Find the price of before VAT was added.**

**Solution.**

**Question. 82 Kritika ordered one pizza and one garlic bread from a pizza store and paid Rs 387 inclusive of taxes of Rs 43. Find the tax%.**

**Solution.**

**Question. 83 Arunima bought household items whose marked price and discount % is as follows**

**Find the total amount of the bill she has to pay.**

**Solution.**

**Question. 84 Devangi’s phone subscription charges for the period 17-02-09 to 16-03-09 were as follows**

**Find the final bill amount, if 3% education cess was also charged on service tax.**

**Solution.**

**Question. 85 If principal = Rs 100000, rate of interest = 10% compounded half-yearly. Find.**

**(a) Interest for 6 months. (b) Amount after 6 months.**

**(c) Interest for next 6 months, (d) Amount after one year.**

**Solution.**

**Question. 86 Babita bought 160 kg of mangoes at Rs 48 per kg. She sold 70% of the mangoes at Rs 70 per kg and the remaining mangoes at Rs 40 per kg. Find Babita’s gain or loss per cent on the whole dealing.**

**Solution.**

**Question. 87 A shopkeeper was selling all his items at 25% discount. During the off season, he offered 30% discount over and above the existing discount. If Pragya bought a skirt which was marked for Rs 1200, how much did she pay for it?**

**Solution.**

**Question. 88 Ayesha announced a festival discount of 25% on all the items in her mobile phone shop. Ramandeep bought a mobile phone for himself. He got a discount of ? 1960. What was the marked price of the mobile phone?**

**Solution.**

**Question. 89 Find the difference between compound interest and simple interest on Rs 45000 at 12% per annum for 5 yr.**

**Solution.**

**Question. 90 A new computer costs Rs 100000. The depredation of computers is very high as new models with better technological advantages are coming into the market. The depredation is as high as 50% every year. How much will the cost of computer be after two years?**

**Solution.**

**Question. 91 The population of a town was decreasing every year due to migration, poverty and unemployment. The present population of the town is 631680. Last year the migration was 4% and the year before last, it was 6%. What was the population two years ago?**

**Solution.**

**Question. 92 Lemons were bought at Rs 48 per dozen and sold at the rate of Rs 40 per 10. Find the gain or loss per cent.**

**Solution.**

**Question. 93 If the price of petrol, diesel and LPG is slashed as follows**

**Complete the above table.**

**Solution**.

**Question. 94 What is the percentage increase or decrease in the number of seats won by A, B, C and D in the general elections of 2009 as compared to the results of 2004?**

**Solution.**

**Question. 95 How much more per cent seats were won by X as compared to Y in assembly election in the state based on the data given below?**

**Solution.**

**Question. 96 Ashima sold two coolers for ? 3990 each. On selling one cooler she gained 5% and on selling the other she suffered a loss of 5%. Find her overall gain or loss % in whole transaction.**

**Solution.**

**Question. 97 A lady buys some pencils for Rs 3 and an equal number for Rs 6. She sells them for Rs 7. Find her gain or loss %.**

**Solution.**

**Question. 98 On selling a chair of Rs 736, a shopkeeper suffers a loss of 8%. At what price should he sell it, so as to gain 8%?**

**Solution.**

**Question. 99 A dining table is purchased for Rs 3200 and sold at a gain of 6%. If a customer pays sales tax at the rate of 5%. How much does the customer pay in all for the table?**

**Solution.**

**Question. 100 Achal bought a second hand car for Rs 225000 and spend Rs 25000 for repairing. If she sold.it for Rs 325000, what is his profit per cent?**

**Solution.**

**Question. 101 A lady bought an air-conditioner for Rs 15200 and spent Rs 300 and Rs 500 on its transportation and repair, respectively. At what price should she sell it to make a gain of 15%?**

**Solution.**

**Question. 102 What price should a shopkeeper mark on a article that costs him Rs 600 to gain 20%, after allowing a discount of 10%?**

**Solution.**

**Question. 103 Brinda purchased 18 coats at the rate of Rs 1500 each and sold them at a profit of 6%. If customer is to pay sales tax at the rate of 4%, how much will one coat cost to the customer and what will be the total profit earned by Brinda after selling all coats?**

**Solution.**

**Question. 104 Film borrowed Rs 1024000 from a bank for one year. If the bank charges interest of 5% per annum, compounded half-yearly, what amount will he have to pay after the given time period. Also, find the interest paid by him.**

**Solution.**

**Question. 105 The following items are purchased from showroom T-Shirt worth Rs 1200 Jeans worth Rs 1000 2 skirts worth Rs 1350 each.****What will these items cost to Shikha if the sales tax is 7%?**

**Solution.**

**Question. 106 The food labels given below information about 2 types of soup cream of tomato and sweet corn. Use these labels to answer the given questions, (all the servings are based on a 2000 calories diet.)**

**(a) Which can be measured more accurately the total amount of fat it cream of tomato soup or the total amount of fat in sweet corn soup? Explain.**

**(b) On serving of cream of tomato soup contains 29% of the recommended daily value of sodium for a 2000 calories diet. What is the recommended daily value of sodium in milligrams? Express the answer up to 2 decimal places.**

**(c) Find the increase per cent of sugar consumed, if cream of tomato soup is chosen over sweet corn soup.**

**(d) Calculate ratio of calories from fat in sweet corn soup to the calories from fat in cream of tomato soup.**

**Solution.**

**Question. 107 Music CD originally priced at Rs 120 is on sale for 25% off. What is the SP? Sonia and Rahul have different ways of calculating the sale price for the items they bought.**

**As you work on the next problem, try both of these methods to see which your refer.**

**Solution.**

**Question. 108 Store A and store B both charge Rs 750 for a video game. This week the video game is on sale Rs 600 at store B and for 25% off at store A. At which store is the game less expensive?**

**Solution.**

**Question. 109 At a toy shop price of all the toys is reduced to 66% of the original price.**

**(a) What is the sale price of a toy that originally costs Rs 90?**

**(b) How much money would you save on a toy costing Rs 90?**

**Solution.**

**Question. 110 A store is having a 25% discount sale. Sheela has a Rs 50 gift voucher and wants to use it to buy a board game marked for Rs 320. She is not sure how to calculate the concession she will get. The sales clerk has suggested two ways to calculate the amount payable.**

**Method 1 Subtract Rs 50 from the price and take 25% off the resulting price.**

**Method 2 Take 25% off the original price and then subtract Rs 50.**

**(a) Do you think both the methods will give the same result? If not, predict which method will be beneficial for her.**

**(b) For each method, calculate the amount Sheela would have to pay. Show your work.**

**(c) Which method do you think stores actually use? Why?**

**Solution.**

**Question. 111 Living on your own Sanjay is looking for one bedroom appartment on rent. At Neelgiri appartments, rent for the first two months is 20% off. The one bedroom rate at Neelgiri is Rs 6000 per month. At Savana appartments, the first month is 50% off. The one bedroom rate at Savana appartments is Rs 7000 per month. Which appartment will be cheaper for the first two months? By how much?**

**Solution.**

**Question. 112 For an amount, explain why, a 20% increase followed by a 20% decrease is less than the original amount.**

**Solution.**

**Question. 113 Sunscreens block harmful ultraviolet (UV) rays produced by the sun. Each sunscreen has a Sun Protection Factor (SPF) that tells you how many minutes you can stay in the sun before you receive one minute of burning UV rays. e.g. If you apply sunscreen with SPF 15, you get one minute of UV rays for every 15 minutes you stay in the sun.**

**(i) A sunscreen with SPF 15 allows only \(\frac { 1 }{ 15 } \) of the sun’s UV rays. What per cent of UV rays does the sunscreen abort?**

**(ii) Suppose, a sunscreen allows 25% of the sun’s UV rays.**

**(a) What fraction of UV rays does this sunscreen block? Give your answer in lowest terms.**

**(b) Use your answer from part (a) calculate this sun screen’s SPF. Explain how you found your answer?**

**(iii) A label on a sunscreen with SPF 30 claims that the sunscreen blocks , about 97% of harmful UV rays. Assuming the SPF factor is accurate,is this claim true. Explain.**

**Solution.**

**Question. 114 A real estate agent receives Rs 50000 as commission, which is 4% of the selling price. At what price does the agent sell the property?**

**Solution.**

**Question. 115 With the decrease in prices of tea by 15%, Tonu, the chaiwallah, was able to buy 2 kg jnore of tea with the same Rs 45 that he spent each month on buying tea leaves for his chai shop. What was the reduced price of tea? What was the original price of tea?**

**Solution.**

**Question. 116 Below is the report card of Vidit Atrey. Vidit’s teacher left the last column blank. Vidit is not able to make out, in which subject he performed better and in which he needs improvement. Complete the table to help Vidit know his comparative performance.Assessment report for- 2009-2010**

**Solution.**

**Question. 117 Sita’s practicing basket ball. She has managed to score 32 baskets in 35 attempts. What is her success rate in percentage?**

**Solution.**

**Question. 118 During school hours, Neha finished 73% of her homework and Minakshi completed \(\frac { 5 }{ 8 } \) of her, homework. Who must finish a greater per cent of 8 homework?**

**Solution.**

**Question. 119 Rain forests are home to 90000 of the 250000 identified plant species in the world. What per cent of the world’s identified plant species are found in rain forests?**

**Solution.**

**Question. 120 Madhu’s room measures 6m x 3m. Her carpet covers 8 \({ m }^{ 2 }\). What per t cent of floor is covered by the carpet?**

**Solution.**

**Question. 121 The human body is made up mostly of water. In fact about 67% of a person total body weight is water. If Jyoti weights 56 kg, how much of her weight is water?**

**Solution.**

**Question. 122 The per cent of pure gold in 14 carat gold is about 58.3%. A 14 carat gold ring weights 7.6 grams. How many grams of pure gold are in the ring?**

**Solution.**

**Question. 123 A student used the proportion \({ n }^{ 100 }\)=\({ 5 }^{ 32 }\) to find 5% of 32. What did the student do wrong?**

**Solution.**

**Question. 124 The table shows the cost of sunscreen of two brands with and without sales tax. Which brand has a greater sales tax rate? Give the sales tax rate of each brand?**

**Solution.**

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