### Question 4

SSC-CGL 2018 June 4 Shift 2

Renu bought an item for 1,240 and sold it at a loss of 25%. With that amount, she bought another item and sold it for 40% profit. What percentage of profit did Renu get?

- 12
- 5
- 6-2/3
- 15

### Solution 1

Let the original CP be Rs. 100. So first sale price at 25% loss is Rs. 75. The second sale price at a gain of 40% is (75 + 40% of 75) = 105 Rs. The overall profit is (105 - 100 = Rs. 5), or 5% answer!

### Solution 2

We can think of 2 successive "discounts" of (-)25% and (+)40%. The effective "% discount" is [(1 - 0.25) x (1 + 0.4) - 1]x 100 = 0.75 x 1.4 x 100% = 5% answer!

EXPLANATION: effective % discount after 2 successive discounts of $\displaystyle r_1 \text{ and } r_2$ percent is $\displaystyle (1 - r_1)(1 - r_2) - 1$. You should remember this shortcut formula.### Solution 3

Loss of 25% means a loss of $\displaystyle \frac14 \times 1240$ = 310 Rs.

So the first sale is 1240 - 310 = Rs. 930

In the next transaction there is a profit of 40%, i.e., of $\displaystyle \frac 25 \times 930$ = 372 Rs.

The overall profit stands at 372 - 310 = 62 Rs.

Overall % profit is $\displaystyle \frac{62}{1240} \times 100 = 5\% \:\underline{Ans}$

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