The income of A, B and C are in the ratio 7 : 9 : 12 and their spending are in the ratio 8 : 9 : 15. If A saves $$\frac{1}{4}$$ th of his income then the savings of A, B and C are in the ratio of = ?
a) 56 : 99 : 69
b) 69 : 56 : 99
c) 99 : 56 : 69
d) 99 : 69 : 56

Answer: a
Explanation: Let income of A, B and C are 7x, 9x and 12x respectively
and expenditure of A, B and C are 8y, 9y and 15y respectively
$$\eqalign{ & \Rightarrow {\text{Income}}\,{\text{of,}} \cr & A \times \frac{1}{4} = {\text{Saving}}\,{\text{of}}\,{\text{A}}\,\left( {{\text{given}}} \right) \cr & 7x – 8y = 7x \times \frac{1}{4} \cr & 28x – 32y = 7x \cr & 21x = 32y \cr & x:y = 32:21 \cr} $$
The ratio of savings of A, B and C
⇒ (7x – 8y) : (9x – 9y) : (12x – 15y)
⇒ (7 × 32 – 8 × 21) : (9 × 32 – 9 × 21) : (12 × 32 – 15 × 21)
⇒ (224 – 168) : (288 – 189) : (384 – 315)
⇒ 56 : 99 : 69