The monthly expenses of a person are 66 \displaystyle\frac{2}{3}\% more than her monthly savings. If her monthly income increases by 44% and her monthly expenses increases by 60%, then there is an increase of ₹1,040 in her monthly savings. What is the initial expenditure (in ₹)?

(a) 9,000

(b) 12,000

(c) 10,000

(d) 13,000

{Previously asked in SSC CGL Mains 2020}

**Ans**: (c) 10,000

**Explanation**:

66 \displaystyle\frac{2}{3}\%\uparrow = \displaystyle\frac{2}{3} \Rightarrow Increment of 2 on 3

44\%\uparrow = \displaystyle\frac{11}{25} \Rightarrow Increment of 11 on 25

60\%\uparrow = \displaystyle\frac{3}{5} \Rightarrow Increment of 3 on 5

If savings is 3, expenditure will be 3 + 2 = 5

Hence, income = expenditure + savings = 5 + 3 = 8

Income is 40% increased, i.e. it become \displaystyle\frac{11+25}{25} = \displaystyle\frac{36}{25}th of original income 8

Same happens to new expenditure.

To avoid fraction let’s multiply the ratios by LCM (25, 5) = 25

Difference in savings = 88 – 75 = 13

∴ 13 part = 1040

\Rightarrow 125 part = 80 × 125

\qquad\qquad\ = 10000

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