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?

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Step 1: Let the incomes of P, Q, and R be 10x, 12x, and 9x respectively.

Step 2: Let the expenditures of P, Q, and R be 12y, 15y, and 8y respectively.

Step 3: Given that Q saves 25% of his income.
Savings of Q = 25% of income of Q = 0.25 * 12x = 3x

Step 4: Savings of Q can also be calculated as income - expenditure.
So, savings of Q = income of Q - expenditure of Q
3x = 12x - 15y
=> 15y = 12x - 3x = 9x
=> y = 9x / 15 = 3x / 5

Step 5: Calculate savings of P and R using y = 3x/5.
Savings of P = income of P - expenditure of P = 10x - 12y = 10x - 12*(3x/5) = 10x - (36x/5) = (50x/5) - (36x/5) = 14x/5
Savings of R = income of R - expenditure of R = 9x - 8y = 9x - 8*(3x/5) = 9x - (24x/5) = (45x/5) - (24x/5) = 21x/5

Step 6: Now, savings ratio of P : Q : R = (14x/5) : 3x : (21x/5)
Multiply all terms by 5 to clear denominator:
= 14x : 15x : 21x
Cancel x:
= 14 : 15 : 21

Step 7: Match with options. The correct ratio is 14 : 15 : 21 which corresponds to option 2.

Note: The provided answer options show option 4 as correct (21 : 14 : 15), but the correct calculation yields 14 : 15 : 21, which is option 2.

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