Exercise : 1


1. Salaries of A, B and C were in the ratio of 3 : 5 : 7 respectively. If their salaries were increased by 50%, 60% and 50% respectively, what will be the new ratio of their respective salaries?
(a) 3 : 6 : 7
(b) 4 : 5 : 7
(c) 4 : 5 : 8
(d) Data inadequate
(e) None of these
Ans.e

Suppose the salaries of A, B and C were 300k, 500k and 700k respectively.

After increment salary of

A = 300k + 50% of 300k = 450k

B = 500k + 60% of 500k = 800k

C = 700k + 50% of 700k = 1050k

Hence, new ratio of the respective salaries of A, B and C = 450k : 800k : 1050k = 9 : 16 : 21

2. If 40% of a number is equal to two-thirds of another number, what is the ratio of the first number to the second?
(a) 7 : 3
(b) 3 : 7
(c) 2 : 5
(d) 5 : 3
(e) None of these
Ans.d

Suppose the first number is x and the second numbery.

Therefore, 40% of x = 23 of y

xy = 23 × 10040 = 53

3. Radha started a business, investing 75,000. After 3 months, Sunidhi joined her with an amount of 1,25,000 and after another six months Neha joined them with an amount of 1,50,000. Profit earned at the end of three years from when Radha started the business should be distributed in what ratio among Radha, Sunidhi and Neha respectively?
(a) 36 : 55 : 54
(b) 18 : 28 : 27
(c) 35 : 54 : 55
(d) Cannot be determined
(e) None of these
Ans.a

Ratio of their profits (Radha’s : Sunidhi’s : Neha’s)

= 75 × 36 : 125 × 33 : 150 × 27

= 3 × 36 : 5 × 33 : 6 × 27

= 3 × 12 : 5 × 11 : 6 × 9

= 36 : 55 : 54

4. What should come in place of the question mark(?) in the following equation? 28? = ?112
(a) 70
(b) 56
(c) 48
(d) 64
(e) None of these
Ans.b

28? = ?112

\ ? = \(\sqrt{28 \times 112} = 56\)

5. An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled with B type of petrol. At this time, what was the percentage of A type of petrol in the tank?
(a) 50%
(b) 40%
(c) 33.5%
(d) 37.5%
(e) None of these
Ans.d

Petrol A Petrol B
I A 0
II A2 B2
III A4 + A2 B4
IV A8 + A4 B8 + B2

Now, amount of petrol A = A4 + A8 = 3A8

∴ required% = 3A⁄ (8 × A) × 100 = 37.50%

6. The ratio of A’s and B’s salary is 9 : 4. If A’s salary is increased by 15%, then his total salary becomes 5175. What is the salary of B?
(a) 2,000
(b) 4,000
(c) 4,500
(d) 2,500
(e) None of these
Ans.a

Let the salaries of A and B be 9x and 4x.

9x × 115100 = 5175

\ x = 500

\ salary of B = 500 × 4 = 2000

7. Three friends A, Band C started a business by investing a sum of money in the ratio of 5 : 7 : 6. After 6 months C withdraws half of his capital. If the sum invested by ‘A’ is 40,000, out of a total annual profit of 33,000, C’s share will be
(a) 9,000
(b) 12,000
(c) 11,000
(d) 10,000
(e) None of these
Ans.a

Sum invested by A, B and C is

5 × 12 : 7 × 12 : 6 × 6 + 3 × 6

or, 60 : 84 : 54 or, 10 : 14 : 9

\Share of C = 933 × 33,000 = 9,000

8. Seats for Maths, Physics and Biology are in the ratio of 5 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?
(a) 2 : 3 : 4
(b) 6 : 7 : 8
(c) 6 : 8 : 9
(d) Cannot be determined
(e) None of these
Ans.a

Reqd ratio 5 × 140100 : 7 × 150100 : 8 × 175100

= 5 × 140 : 7 × 150 : 8 × 175 = 2 : 3 : 4

9. Mr Sharad started a business investing 50000. Four months later Mr Praveen joined the business by investing 90000. If the profit in the business at the end of the year was 22000 how much amount would Mr Praveen have received as the profit?
(a) 16000
(b) 14000
(c) 12000
(d) 11000
(e) None of these
Ans.c

Ratio of their investment

= 50000 × 12 : 90000 × 8 = 5 : 6

\ Amount received by Praveen = 611 × 22,000

= 12,000

10. The ratio of Gomati’s and Rashmi’s ages is 3 : 5 respectively. After ten years this ratio will become 2 : 3. What is Rashmi’s age in years?
(a) 50
(b) 40
(c) 60
(d) Cannot be determined
(e) None of these
Ans.a

Quicker Method : After 10 years, the ratio of Gomati and Rashmi’s ages is 2 : 3. We can also write 2 : 3 as 4 : 6. Now, difference in the ratio is I in both the cases.

Therefore, 1 = 10

∴ 5 → 5 × 10 = 50 years.