Question : Soham’s initial expenditure and savings were in the ratio of 5 : 3. His income increased by 25%. If his initial savings were Rs. 4,500, find his income (in Rs.) after the increment.
Option 1: 16,000
Option 2: 15,000
Option 3: 9,375
Option 4: 12,000
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Correct Answer: 15,000
Solution :
Let denote the initial expenditure as $E$, initial savings as $S$, and the initial income as $I$.
Given that the ratio of expenditure to savings is 5 : 3.
$E : S = 5 : 3$
⇒ $E = \frac{5}{3}S$
$I = E + S$
⇒ $I = \frac{5}{3}S + S = \frac{8}{3}S$
The initial savings S were Rs. 4,500.
So, $I = \frac{8}{3} \times 4500 = 12,000$
The income increases by 25%, the income after the increment $I'$.
$I' = I + 0.25I = 12000 + 0.25 \times 12000 =$ Rs. 15,000
Hence, the correct answer is 15,000.
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