Question

The ratio of incomes of A, B, and C is 3 : 5 : 12 and the ratio of their expenditures is 1 : 2 : 6. If C saves one-fourth of his income, then find the ratio of their savings.
1. 1 : 4 : 5
2. 3 : 4 : 6
3. 2 : 4 : 5
4. 4 : 5 : 6
5. 2 : 5 : 7

Answer 1

Correct Answer - Option 2 : 3 : 4 : 6

Given:

Income ratio = 3 : 5 : 12

Expenditure ratio = 1 : 2 : 6

C's savings = 1/4 of income

Calculation:

Let the incomes be 3x, 5x, 12x

and expenditure be y, 2y, 6y

A.T.Q

12x - 6y = 1/4 × 12x 

⇒ 9x = 6y

⇒ x : y = 2 : 3

Income = 6 ratio, 10 ratio, 24 ratio

Expenditure = 3 ratio, 6 ratio, 18 ratio

Savings = (6 - 3) : (10 - 6) : (24 - 18)

⇒ 3 : 4 : 6

∴ The answer is 3 : 4 : 6