1.3 Marks

The price of diesel has increased by 20%. By what percent should Mr. Kulkarnireduce the consumption of diesel so that his monthly budget is not affected?

1) 25%

2) 20%

3) 16.66%

4) 12.25%

5) 10.22%

Solution:The price of diesel increases by 20%.

Hence, option 3.

2.3 Marks

If the price of rice falls down by 25%, by how much percent should a family increaseits consumption, so as not to decrease expenditure.

1) 25%

2) 16.66%

3) 33.33%

4) 36%

5) 20.25%

Solution:The price of rice falls down by 25%.

Hence, option 3.

3.3 Marks Ganesh sells his goods 30% cheaper than Himesh and 20% dearer than Shiva. How

much percentage are Shiva’s goods cheaper than Himesh’s?

1) 50.33%

2) 41.67%

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Section I

3) 50%

4) 28.14%

5) 25%

Solution:Let Ganesh sells his goods at Rs. 100

Hence, option 2.

4.3 Marks

Shekhar’s salary is 33.33% more than Abhijeet’s salary. By what percentage isAbhijeet’s salary less than Shekhar’s salary?

1) 25%

2) 30%

3) 22.22%

4) 20%

5) 16.66%

Solution:

Let Abhijeet’s salary be Rs. 100

∴ Shekhar’s salary = Rs. 133.33

Hence, option 1.

5.3 Marks

Vijay spends 45% of his salary on his brother’s education, 20% of the rest on rentand 14% of the total salary on travelling. After his expenditure, he is left with Rs.4500. What is Vijay’s salary?

1) Rs. 21428.57

2) Rs. 18546.52

3) Rs. 12000

4) Rs. 1000

4) Rs. 1000

5) Rs. 15000

Solution:

Let Vijay’s salary be Rs. x

He spends Rs. 0.45x on his brother’s education.

He spends 20% of the rest i.e. 0.2 × (x − 0.45x) = Rs. 0.11x on rent.

Finally, he spends Rs. 0.14x on travelling.

∴ x – 0.45x – 0.11x – 0.14x = 4500

∴ 0.3x = 4500

∴ x = Rs. 15,000

∴ Vijay’s salary is Rs. 15,000.

Hence, option 5.

6.3 Marks

In a school, 70% of the students are boys and the rest are girls. Further 20% of theboys and 30% of the girls are getting a fee waiver. If this number is 230, find the totalnumber of students getting 33% concession if it is a rule that 40% of those not gettinga fee waiver are eligible to get one-third fee concession?

1) 170

2) 308

3) 210

4) 240

5) 320

Solution:

Let the total number of students in the school be x.

∴ Number of boys is 0.7x and number of girls is 0.3x.

From the given data,

(0.2 × 0.7x) + (0.3 × 0.3x) = 230

∴ x = 1000

Number of students who do not get a waiver = 1000 − 230 = 770

∴ Number of students eligible for one-third fee concession = 0.4 × 770 = 308

Hence, option 2.

7.3 Marks

Laxmi goes to a shop to buy a toy kitchen set costing Rs. 3500. The rate of sales taxis 12%. The shop-keeper however reduces the price and she pays Rs. 3500

3 Marks

is 12%. The shop-keeper however reduces the price and she pays Rs. 3500inclusive of sales tax. Find the percentage reduction in the price.

1) 7.25%

2) 11.25%

3) 10.71%

4) 9.75%

5) 9.24%

Solution:

Let the shop-keeper reduce the price of kitchen-set to Rs. x

Hence, option 3.

8.3 Marks

P’s salary is first decreased by 30% and then increased by 25%. The result is thesame as Q’s salary decreased by 25% and increased by 30%. Find the ratio of P’ssalary to that of Q’s?

1)

2)

3)

4)

5)

Solution:

Let P’s salary be Rs. p and Q’s salary be Rs. q.

P’s salary is first decreased by 30% and then increased by 25%.

∴ p → 0.7p → 0.875p

Q’s salary is first decreased by 25% and then increased by 30%.

∴ q →0.75q → 0.975q

From the given data,

0.875p = 0.975q

Hence, option 4.

9.3 Marks

Palm Royal building has three wings A, B and C. The number of families in the threewings A, B and C is in the ratio 12 : 15 : 10. In wing A, 65% of the families arevegetarian, in wing B, 40% of the families are non-vegetarian. If 75% of the familiesin wing C are vegetarian, find the percentage of non-vegetarian families in PalmRoyal.

1) 34.32%

2) 33.33%

3) 40%

4) 25%

5) None of these

Solution:

Let the number of families in the three wings A, B and C be 12x, 15x and 10xrespectively.

In wing A,

Number of vegetarian families = 0.65 × 12x = 7.8x

∴ Number of non-vegetarian families = 12x − 7.8x = 4.2x

In wing B,

Number of non-vegetarian families = 0.4 × 15x = 6x

In wing C,

Number of vegetarian families = 0.75 × 10x = 7.5x

∴ Number of non-vegetarian families = 10x − 7.5x = 2.5x

Hence, option 1.

10.3 Marks

Two numbers A and B are 16% and 45% greater than a third number C. Find by whatpercentage is the number A less than number B?

1) 10%

2) 20%

3) 30%

4) 15%

5) 25%

Solution:A = 1.16C and B = 1.45C

Hence, option 2.

11.3 Marks

The marked price of a sofa is Rs. 2300, which is 15% above the cost price. It is soldat a discount of 5% on the marked price. Find the profit percent.

1) 5.75%

2) 6.5%

3) 8.25%

4) 9.25%

5) None of these

Solution:

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

The marked price of the sofa is Rs. 2300, which is 15% above the cost price.

∴ 1.15x = 2300

∴ x = Rs. 2000

The sofa is sold at a discount of 5% on the marked price.

∴ Selling price of the sofa = 2300 − 0.05 × 2300 = Rs. 2185

Hence, option 4.

12.3 Marks

A whole-seller allows a discount of 30% on the list price of an article to a retailer. Theretailer sells this article to the customer at a discount of 8% on the list price. If thecustomer paid Rs. 115 for the article, what is the profit made by the retailer?

1) Rs. 20

2) Rs. 25

3) Rs. 27.5

4) Rs. 32.5

5) Rs. 36.5

Solution:

Let the list price of the article be Rs. x

The customer buys this article for Rs. 115 which is equal to 8% discount on the listprice.

∴ 0.92x = 115

∴ x = Rs. 125

A whole-seller allows a discount of 30% on the list price to a retailer.

∴ The retailer buys this article for (0.7 × 125) = Rs. 87.5

∴ Profit made by the retailer = 115 – 87.5 = Rs. 27.5

Hence, option 3.

13.3 Marks

A reduction of 12% in the price of oil enables Mrs. Shanti to buy 5.6 litres more forRs. 840. Find the reduced price per litre.

1) Rs. 15

2) Rs. 18

3) Rs. 21.5

4) Rs. 24.5

5) None of these

Solution:

The price of oil reduces by 12%.

Let the original consumption be x litres.

∴ 13.63% of x = 5.6

∴ x = 41.08 litres.

∴ Reduced price = 0.88 × 20.5 = Rs. 18.04 ≈ Rs. 18

Hence, option 2.

14.3 Marks

A sold a cycle to B at a profit of 18%. Later on, B sold it back to A at a profit of 50%,thereby gaining Rs. 236. How much did A pay for the cycle originally?

1) Rs. 250

1) Rs. 250

2) Rs. 325

3) Rs. 400

4) Rs. 450

5) Rs. 600

Solution:

Let the original price of cycle be Rs. x

∴ A sold a cycle to B at Rs. 1.18x and B sold it back to A at Rs. 1.18x × 1.50 =1.77x.

∴ B’s profit = 1.77x – 1.18x = 236

i.e. 0.59x = 236

∴ x = Rs. 400

Hence, option 3.

15.3 Marks

A dealer sold two cell-phones for Rs. 5400 each, gaining 25% on one and losing25% on the other set. Find his net gain or net loss.

1) Rs. 240 loss

2) Rs. 720 gain

3) Rs. 480 loss

4) Rs. 600 gain

5) Rs. 720 loss

Solution:

For the first cell-phone,

S.P1 = Rs. 5400

Profit = 25%

For the second cell-phone,

S.P2 = Rs. 5400

Loss = 25%

∴ Total C.P = Rs. 11520

Total S.P = Rs. 10800

∴ Loss = Rs. 720

Hence, option 5.

16.3 Marks

A shopkeeper allows a discount of 12% on the list price of a certain article. He furtherallows a discount of 12% for customers who buy it on a Sunday. Calculate the amountpaid by a customer for the article, the list price of which is Rs. 5000, if he buys it on aSunday.

1) Rs. 3928

2) Rs. 4400

3) Rs. 3642

4) Rs. 3872

5) Rs. 4000

Solution:Since the customer buys the article on a Sunday, he gets a discount of 12% followedby another discount if 12%.

Hence, option 4.

17.3 Marks

The cost of running the printing machine is Rs. 150 per 100 copies. The cost ofpaper, ink etc. is 80 paise per copy. The textbooks are sold at Rs. 5 each. 550copies are printed, but only 240 copies are sold. What is the sum to be obtained toget a profit of 20% is on the cost?

1) Rs. 542

2) Rs. 318

3) Rs. 628

4) Rs. 656

5) Rs. 704

Solution:

Cost of printing 550copies = Rs. 825

Total cost = 825 + 440 = Rs. 1265

∵ 240 copies are sold at Rs. 5 each

∴ Total selling price = Rs. 1200

∴ The sum to be obtained to get a profit of 20% on the cost = (1.2 × 1265) – 1200 =

Rs. 318.

Hence, option 2.

18.3 Marks

Rani goes to a shop to purchase a cell phone priced at Rs. 1200. The shop-keeperoffers her 4 discount options. Help her choose the option which offers her maximumdiscount.

1) 2 successive discount of 20% each

2) 2 successive discount of 25% and 15%

3) Single discount of 35%

4) 2 successive discount of 30% and 5%

5) Either 3 or 4

Solution:

Consider option 1:

Consider option 2:

Consider option 3:

Discount = 35%

Consider option 4:

Hence, option 2.

19.3 Marks

A TV dealer sells TV sets at Rs. 6500 per TV. On a particular day, he is forced togive two successive discounts of 15% and 10% respectively, to a customer.However, he recovers the sales tax on the net sale price from the customer at 8% ofthe net price. At what price does the TV dealer sell the TV to the customer?

1) Rs. 5370.3

2) Rs. 5470.3

3) Rs. 5385.7

4) Rs. 5485.7

5) Rs. 5296.8

Solution:

∴ S.P of the TV set after the discount is offered = 0.765 × 6500 = Rs. 4972.5

The shop-keeper recovers 8% sales tax on Rs. 4972.5

∴ The customer has to pay = 1.08 × 4972.5 = Rs. 5370.3

Hence, option 1.

20.3 Marks

The SI on a sum of money is 20% of the principal, and the rate per annum is equal toone fifth of the number of years. Find the rate percent.

1) 2%

2) 4%

3) 5%

4) 10%

5) 12%

Solution:

It is given that SI = 0.2P

Now, using the SI formula,

R2 = 4

∴ R = 2%

Hence, option 1.

21.

3 Marks

Interest obtained on a sum of Rs. 7500 for 5 years is Rs. 1875. Find the rate percent.

1) 15%

2) 10%

3) 5%

4) 8%

5) 3%

Solution:

Solution:

R = 5%

Hence, option 3.

22.3 Marks

Find the amount after 5 years if Rs. 2500 is lent out at 10% per annum simple interestfor 5 years.

1) Rs. 3250

2) Rs. 3750

3) Rs. 4050

4) Rs. 4250

5) Rs. 4500

Solution:

∴ A = P + I = 2500 + 1250 = Rs. 3750

Hence, option 2.

23.3 Marks

Find the amount after two years if Rs. 3200 is lent at compound interest at 10% perannum for 3 years.

1) Rs. 4160

2) Rs. 4200

3) Rs. 4080.2

4) Rs. 4425.2

5) Rs. 4259.2

Solution:

A = Rs. 4259.2

Hence, option 5.

Hence, option 5.

24.3 Marks

The amount after 4 years of simple interest on a capital of Rs. 1800 is Rs. 2952. Findthe rate of interest.

1) 6%

2) 8%

3) 12%

4) 16%

5) 18%

Solution:

SI = A – P = 2952 – 1800 = Rs. 1152

Hence, option 4.

25.3 Marks

The amount repaid after two years at compound interest is Rs. 3168. Which of thefollowing is the value of the principal and the rate?

1) Rs. 2800, 6%

2) Rs. 2600, 10%

3) Rs. 2400, 15%

4) Rs. 2200, 20%

5) None of these

Solution:

This question can be solved by using the options as follows,

Hence, option 4.

Group Question

Answer the following questions based on the information given below.

26.3 Marks

Find the difference between the simple and the compound interest at 25% perannum for 2 years on a principal of Rs. 4400.

1) Rs. 325

2) Rs. 275

3) Rs. 250

4) Rs. 225

5) Rs. 175

Solution:

CI – SI = 2475 – 2200 = Rs. 275

Hence, option 2.

27.3 Marks

After how many years will a sum of Rs. 5400 becomes Rs. 7560 at the rate of 5% perannum?

1) 5

2) 6

3) 8

4) 10

5) 12

Solution:

SI = A – P = 7560 – 5400 = Rs. 2160

Hence, option 3.

28.3 Marks

What is the difference between the simple interest on a principal of Rs. 750 beingcalculated at 8% per annum for 7 years and 6% per annum for 8 years?

1) Rs. 60

2) Rs. 75

3) Rs. 45

4) Rs. 90

5) Rs. 105

Solution:

Hence, option 1.

29.3 Marks

What is the simple interest on a sum of Rs. 1400 if the rate of interest for the first 4years is 5% per annum and for the last 3 years is 3% per annum?

1) Rs. 356

2) Rs. 372

3) Rs. 392

4) Rs. 406

5) Rs. 426

Solution:

Hence, option 4.

30.3 Marks

What is the simple interest for 11 years on a sum of Rs. 2000 if the rate of interest forthe first 5 years is 10% per annum and for the last 5 years is 20% per annum?

1) Rs. 3000

2) Rs. 3200

3) Rs. 3400

4) Rs. 3500

5) Cannot be determined

Solution:

Since the rate for the 6th year is not known, it is not possible to find the simpleinterest.

Hence, option 5.

31.3 Marks

What is the difference between compound interest and simple interest for the sum ofRs. 2500 over a 2 year period if the compound interest is calculated at 15% andsimple interest is calculated at 16%?

1) Rs. 1

2) Rs. 3.75

3) Rs. 6.25

4) Rs. 10

5) Rs. 12.5

Solution:

CI = 3306.25 – 2500 = Rs. 806.25

CI – SI = 806.25 – 800 = Rs. 6.25

Hence, option 3.

32.

3 Marks

Find the compound interest on Rs. 600 at the rate of 20% per annum for 18 months

when interest is compounded half-yearly.

1) Rs. 148

2) Rs. 180

3) Rs. 190.2

4) Rs. 198.6

5) Rs. 212.4

Solution:

CI = 798.6 – 600 = Rs. 198.6

Hence, option 4.

33.3 Marks

Find the principal if the interest compounded at the rate of 5% per annum for twoyears is Rs. 1230.

1) Rs. 1000

2) Rs. 11500

3) Rs. 12000

4) Rs. 13500

5) Rs. 14000

Solution:

∴ P = Rs. 12000

Hence, option 3.

34.3 Marks

per annum for two years and the sum becomes Rs. 676.

1) Rs. 600

2) Rs. 576

3) Rs. 542

4) Rs. 512

5) None of these

Solution:

∴ P = Rs. 576

Hence, option 2.

35.3 Marks

Ajay lent Rs. 8000 to Vijay at a compound interest and got Rs. 9261 after threeyears. What is the rate of interest charged by Ajay if the interest is compoundedannually?

1) 5%

2) 6.06%

3) 7.07%

4) 8%

5) 9.09%

Solution:

r = 5%

Hence, option 1.

36.3 Marks

Vinay lent Rs. 25000 to Vini. Vini pays him 12% interest per annum compounded

quarterly. What is the amount that Vinay receives after 21 months?

1) Rs. 28456.4

2) Rs. 29530.6

3) Rs. 30746.8

4) Rs. 31284.2

5) Rs. 32862.4

Solution:

A = Rs. 30746.8

Hence, option 3.

37.3 Marks

Subhash borrows Rs. 2000 from two money lenders. He pays simple interest at therate of 8% per annum to the first moneylender and at the rate of 6% per annum to thesecond. The total interest he pays for the entire year is Rs. 128. How much does heborrow from the second moneylender?

1) Rs. 400

2) Rs. 800

3) Rs. 1200

4) Rs. 1600

5) Rs. 1800

Solution:

Let Subhash borrow Rs. x from the second money lender and Rs. (2000 – x) from thefirst.

∴ x = Rs. 1600

Hence, option 4.

38.3 Marks

Manav derives an annual income of Rs. 396 from Rs. 3000 invested partly at 12%p.a. and partly at 15% p. a. simple interest. How much of his money is invested at

15%.

1) Rs. 2400

2) Rs. 2000

3) Rs. 1800

4) Rs. 1200

5) Rs. 600

Solution:

Let the amount invested by Manav at 15% be Rs. x.

∴ Rs. (3000 – x) is invested at 12%

∴ x = Rs. 1200

Hence, option 4.

39.3 Marks

Mrs. Gandhi lends money at simple interest at 8% per annum for the initial 3 years,12.5% per annum for the next 4 years, 15% per annum after the first 7 years. Find theinterest money Mrs. Gandhi receives if she lends Rs. 27,000 for 12 years.

1) Rs. 40,230

2) Rs. 72200

3) Rs. 80500

4) Rs. 84650

5) None of these

Solution:

Hence, option 1.

40.3 Marks

The population of a city is 50000. If the annual birth rate and the annual death rate are8% and 5% respectively, then calculate the population of the city after 2 years.

1) 58000

2) 56450

3) 53045

4) 54045

5) Cannot be determined

Solution:

Annual birth rate = 8%

Annual death rate = 5%

∴ Population increases by (8 − 5) = 3% every year.

∴ Population of the city after 2 years = (1.03)2 × 50000 = 53045

Hence, option 3.