Exercise 1


1. The income of a company increases 20% per annum. If its income is 2664000 in the year 1999 what was its income in the year 1997?
(a) 2220000
(b) 2850000
(c) 2121000
(d) 1855000
(e) None of these
Ans.e

Let income in 1997 = x

According to the question,

Income in 1998 = x + x5 = 6x5

Income in 1999 = 6x5 + 6x25 = 36x25

But given, income in 1999 = 2664000

36x25 = 2664000 ⇒ x = 1850000

2. If the growth in production of company A from 1994 to 1995 was 25% and that from 1995 to 1996 was 60%, then what percentage growth took place from 1994 to 1996?
(a) 85%
(b) 75%
(c) 200%
(d) 100%
(e) None of these
Ans.d
Percentage growth from 1994 to 1996

= +25 + 60 + \(\frac{25 \times 60}{100}\) = +100%

3. A shopkeeper employed a servant at a monthly salary of 1500. In addition to it, he agreed to pay him a commission of 15% on the monthly sale. How much sale in Rupees should the servant do if he wants his monthly income as 6000?
(a) 30000
(b) 415000
(c) 31500
(d) 50000
(e) None of these
Ans.a
Servant’s commission amount

= 6000 – 1500 = 4500

i.e.,15% = 4500

or,100% = 450015 × 100 = 30000

4. Mr Yadav spends 60% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year were 48456, how much amount per month would he have spent on clothes and transport?
(a) 4038
(b) 8076
(c) 9691.20
(d) 4845.60
(e) None of these
Ans.a

∵ Amount, he have spent in 1 month on clothes transport = Amount spent on saving per month

∵ Amount, spent on clothes and transport

= 4845612 = ₹4038

5. In a class of 60 children, 30% children can speak only English, 20 % Hindi and English both and the rest of the children can speak only Hindi. How many children can speak Hindi?
(a) 42
(b) 36
(c) 30
(d) 48
(e) None of these
Ans.a

Number of students who speak only English

= 30% of 60 = 18

∵ Number of students who speak Hindi and English

= 20% of 60 = 12

∵ Number of students who speak only Hindi

= (60 – 30 =) 30

∵ No. of students who speak Hindi = 30 + 12 = 42

6. Somesh bought a microwave oven and paid 10% less than its original price. He sold it at 30% profit on the price he had paid. What percentage of profit did Somesh earn on the original price?
(a) 32%
(b) 11%
(c) 20%
(d) 17%
(e) None of these
Ans.d
Quicker Method:

% profit which Somesh gets

= –10 +30 – \(\frac{10 \times 30}{100}\) = +17%

7. The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 1988, the price of commodity X was 4.20 and that of Y was 6.30, in which year will commodity X cost 40 paise more than commodity Y?
(a) 1997
(b) 1998
(c) 1999
(d) 2000
(e) None of these
Ans.b

Suppose in ‘n’ years the price of comodity X will be more by 40 paise than that of commodity Y.

∴ 420 + 40n – 630 – 15n = 40

or, 25n – 210 = 40

or, 25n = 250

or, n = 25025 = 10 years.

8. Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 5000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?
(a) 100000
(b) 100500
(c) 105000
(d) Data inadequate
(e) None of these
Ans.c

Let the investment of X in 1995 be ₹x.

∴ Profit = ₹ x5

∴ Income = ₹ (x + x5) = ₹ 65x

Investment of company X in 1996 would be (x – 5000) From the question,

(x - 500) × 126100 = 65x ⇒ x = ₹ 105000

9. The strength of a school increases and decreases every alternate year. It starts with increase by 10% and there-after the percentage of increase/decrease is the same. Which of the following is definitely true about the strength of the school in 2001 as compared to that in 1996?
(a) Increase approximately by 2%
(b) Decrease approximately by 2%
(c) Increase approximately by 20%
(d) Decrease approximately by 20%
(e) None of these
Ans.e

Let the strength of school was x in 1998

∴ strength in 2001 will be

= x110100 × 90100 × 110100 × 90100 × 110100 = 1.07811 x

increment = 1.07811 x – x = 0.07811 x

∴ % increase = 7.811 ≈ 8%

10. Milk contains 5% water.What quantity of pure milk should be added to 10 litres of milk to reduce this to 2% ?
(a) 5 litres
(b) 7 litres
(c) 15 litres
(d) Cannot be determined
(e) None of these
Ans.c

Here required quantity of pure milk = \(\frac{10 \times \left( 5 - 2\right)}{2}\)

= \(\frac{10 \times 3}{2}\) = 15 litres.