Question : The ratio of the expenditure and savings of a person is 4 : 3. His expenditure increases by $\frac{1}{4}$th of his initial savings and his income increases by Rs. 300. If his savings remain the same, then what is his initial expenditure?
Option 1: Rs. 1600
Option 2: Rs. 2000
Option 3: Rs. 1000
Option 4: Rs. 1200
Correct Answer: Rs. 1600
Solution :
Let the expenditure be $4x$ and the Savings be $3x$.
Income = expenditure + savings = $4x + 3x = 7x$
New income = $7x + 300$
New expenditure = $4x + \frac{1}{4}\times 3x=4x + \frac{3x}{4}=\frac{19x}{4}$
New savings = $7x + 300 - \frac{19x}{4}=\frac{28x+1200-19x}{4}=\frac{9x+1200}{4}$
According to the question,
$\frac{9x+1200}{4}=3x$
⇒ $9x+1200=12x$
⇒ $3x=1200$
$\therefore x=400$
The initial expenditure = $4x=4\times400=1600$
Hence, the correct answer is Rs. 1600.
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