### Question 12

SSC-CGL 2020 Mar 4 Shift 2

A's income is 60% less than B and A's expenditure is 60% of B's expenditure. If A's income is 70% of B's expenditure, then find the ratio of savings of A and B.

### Solution in Detail

Let income of B = $\displaystyle 100$ Rs

given A's income is 60% less

$\displaystyle \therefore = 100 - 60\% = 40$

Also given that A's income is $\displaystyle 70\%$ of B's expenditure. Hence, B's expenditure is

$\displaystyle = 40 \times \frac{100}{70} = \frac {400}7\text{. . . (1)}$

B's savings: $\displaystyle 100 - \frac{400}{7} = \frac{300}{7}$

Given that "A's expenditure is 60% of B's expenditure" and "A's income is 70% of B's expenditure". This means that A's savings are 70 - 60 = 10% of B's expenditure!

Hence, A's savings are

$\displaystyle 10\% \text{ of }\frac{400}{7} = \frac{40}{7}$

Ratio of savings A : B is

$\displaystyle \frac{40/7}{300/7} = 2 : 15\:\underline{Ans}$

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