Question : The monthly expenses of a person are $66 \frac{2}{3} \%$ more than her monthly savings. If her monthly income increases by 44% and her monthly expenses increase by 60%, then there is an increase of INR 1,040 in her monthly savings. What is the initial expenditure (in INR)?
Option 1: 10,000
Option 2: 12,000
Option 3: 13,000
Option 4: 9,000
Correct Answer: 10,000
Solution :
The monthly expenses is $66\frac{2}{3}$% more than her monthly savings.
$66\frac{2}{3}\% = \frac{2}{3}$
So,
The monthly expenses = The monthly savings + (The monthly saving) × $\frac{2}{3}$
The monthly expenses = (The monthly saving) × $\frac{5}{3}$
Let the monthly saving = $3x$ and the monthly expenditure = $5x$
The monthly income = $(5x + 3x) = 8x$
Now,
Her monthly income increases = 44%
= $8x \times \frac{144}{100}$
= $\frac{1152x}{100}$
= $11.52x$
Now,
Her monthly expenses increases = 60%
= $5x \times \frac{160}{100}$
= $\frac{800x}{100}$
= $8x$
The savings of the person = $(11.52x - 8x) = 3.52x$
According to the question,
There is an increase in her monthly savings = INR 1040
⇒ $(3.52x - 3x) = 1040$
⇒ $0.52x = 1040$
⇒ $x = \frac{1040}{0.52}$
⇒ $x = 2000$
Now,
The initial expenditure = $5x = 5 \times 2000= 10000$
Hence, the correct answer is INR 10,000.
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