The incomes of P, Q, and R are in the ratio 10 : 12 : 9 and their expenditures are in the ratio 12 : 15 : 8. If Q saves 25% of his income, then what is the ratio of the savings of P, Q and R?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 14 : 15 : 21.
The incomes of P, Q, and R are in the ratio 10 : 12 : 9 = 10x : 12x : 9x and
Their expenditures = 12 : 15 : 8 = 12y : 15y : 8y
We know that,
Savings = Income - expenditure
Savings of P = 10x - 12y
Savings of Q = 12x - 15y
Savings of R = 9x - 8y
Q saves 25% of his income
Savings of Q = 0.25 × 12x = 3x
So,
⇒ 3x = 12x - 15y
⇒ 15y = 9x
⇒ y = 3x/5
So,
Savings of P = 10x - 12y
⇒ 10x - 36x/5
⇒ (50x - 36x)/5 = 14x/5
Savings of R = 9x - 8y
⇒ 9x - 24x/5
⇒ (45x - 24x)/5 = 21x/5
So,
The ratio of their savings = 14x/5 : 3x : 21x/5
⇒ 14x : 15x : 21
⇒ 14 : 15 : 21