### Question 6

SSC-CGL 2018 June 4 Shift 1

Someone sold an item at a loss of 15%. If he sold it for Rs 30.60 more then he would get 9% profit. In order to get 10% profit, he has to sell the item in what amount?

- 128.40
- 130
- 140.25
- 132

### Solution in Detail

Let CP = 100.

Hence SP at 15% loss = 85 Rs.

Also, SP at 9% gain would be Rs. 109.

Difference of SP is 109 - 85 = 24

Use unitary method.

If difference is 24, CP = 100.

for 30.60, CP = $\displaystyle \frac{100}{24} \times 30.60$ Rs.

$\displaystyle \therefore $ CP = 127.50 Rs.

$\displaystyle \therefore $ SP for 10% gain $\displaystyle 127.50 \times \frac{110}{100}$

$\displaystyle = 140.25 \text{ Rs }\:\underline{Ans}$

### Solution by Shortcut

This is a standard question. Shortcut formula can be used to obtain the cost price.

Cost = $\displaystyle \frac{100}{\text{loss} + \text{profit}} \times \Delta \text{S}$

$\displaystyle \therefore \text{Cost }= \frac{100}{15 + 9} \times 30.60$

$\displaystyle \therefore $ CP = 127.50 Rs.

$\displaystyle \therefore $ SP for 10% gain $\displaystyle 127.50 \times \frac{110}{100}$

$\displaystyle = 140.25 \text{ Rs }\:\underline{Ans}$

### Solution 3

We can use wild approximations, though it can be risky sometimes. But no harm if you are short on time.

The profit of 9% is about the same as 10%, since figures are small. So let us estimate the SP for a profit of 9%.

If selling is done at 109 - 85 = 24 Rs. more, the SP is 109 Rs.

Hence for selling at Rs. 30.60 more, the SP would be $\displaystyle \approx \frac{109}{24} \times 30$ = $\displaystyle 109 \times 1.25 \approx 136$

But for 10% gain, the SP should, in any case, be greater. Hence (c) is the answer.

### Solution 4

The algebra classic approach. These methods, though long, are true friends of any topper.

SP for 10% gain be x. Then CP = $\displaystyle \frac{10x}{11}$

So *form the equation (CP - 15% of CP) + 30.60 = (CP + 9% of CP)

Hence, 30.60 = 24 % of CP $\displaystyle \therefore 30.60 = \frac{24}{100} \times \frac{10x}{11}$

$\displaystyle \therefore x = \frac{30.60 \times 100 \times 11}{24 \times 10}$, which gives (c) as the answer.

*EXPLANATION: Sale at 15% loss is (CP - 15% of CP). If we sold at 30.60 more, the SP would become (CP - 15% of CP) + 30.60. But that would be a 9% gain, hence sale at CP + 9% of CP. Equating the two we get the above equation.

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