Question

The incomes of A, B and C are in the ratio 6 : 8 : 5 and their expenditures are in the ratio 5 : 7 : 4. If C saves 40% of her income, then the ratio of savings of A, B and C is:
1. 9 : 11 : 8
2. 1 : 1 : 1
3. 9 : 8 : 11
4. 6 : 7 : 4

Answer 1

Correct Answer - Option 1 : 9 : 11 : 8

Given:

The ratio of incomes of A, B and C are in the ratio 6 : 8 : 5 

Their expenditures are in the ratio 5 : 7 : 4

C saves 40% of her income,

Formula used:

Income = Expenditure + Savings

Calculation:

Let income be 'x' & expenditure be 'y' 

⇒ C's income (5x) = 4y + Savings

C’s saving = (40/100) × 5x = 2x

⇒ C’s income = 4y + Savings

⇒ 5x = 4y + 2x

⇒ 3x = 4y

⇒ x = 4y/3

⇒ A’s savings = Income – Expenditure = 6x - 5y = 6 × 4y/3 - 5y = 3y

⇒ B’s savings = Income - Expenditure = 8x - 7y = 8 × 4y/3 - 7y = 11y/3

⇒ C’s saving = 2x = 2 × 4y/3 = 8y/3

∴ Ratio of savings of A, B and C = 3y : 11y/3 : 8y/3 = 9 : 11 : 8.