# (solved)Question 2 SSC-CGL 2018 June 4 Shift 2

Raju's income is 20% more than his expenditure. If his income increases by 60% and his expenditure increase by 70%, then what percentage of the savings will increase/decrease?
(Rev. 18-Jun-2024)

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### Question 2SSC-CGL 2018 June 4 Shift 2

Raju's income is 20% more than his expenditure. If his income increases by 60% and his expenditure increase by 70%, then what percentage of the savings will increase/decrease?

1. decreases by 2%
2. decreases by 10%
3. increases by 2%
4. increases by 10%

### Solution in Short

Let the current expenditure be Rs. 100. Presently he saves 20% i.e, Rs. 20

New expenditure after 70% increase is Rs. 170. New income is (120 + 60% of 120) = Rs. 192. New savings are 192 - 170 = Rs. 22, which is an increase of 10% from Rs. 20. Hence (d) is the answer!

### Solution in Detail

[1] Raju's current expenditure = Rs. $\displaystyle 100$

His current income is 20% more.

$\displaystyle \implies$ current income = Rs. $\displaystyle 120$

$\displaystyle \therefore$ current savings $\displaystyle 120 - 100 = 20$ Rs.

[2] Income increases by 60%

$\displaystyle \therefore$ becomes $\displaystyle 120 + 60\% \times 120 = 192$

Expenditure increases by 70%

$\displaystyle \therefore$ new expenditure is Rs. 170

New savings are 192 - 170 = 22

% increase $\displaystyle \frac{22 - 20}{20} \times 100 = 10\%$ ans!

### Solution by Algebra

this is the school algebra approach, would be longer, but technically correct.

Current expenditure = x. Current income is (x + 20% of x) = 1.2x, giving current savings = (1.2x - x) = 0.2x

New income is (1.2x + 60% of 1.2x) = 1.92x, and new expenditure = (x + 70% of x) = 1.7x, giving new savings = (1.92x - 1.7x) = 0.22x.

% increase $\displaystyle \frac{0.22x - 0.2x}{0.2x} \times 100 = 10 \% \text{(d) }\:\underline{Ans}$