NIELIT 2017 July Scientist B - Section A: 3

Question

The percentage profit earned by selling an article for Rs. $1,920$ is equal to the percentage loss incurred by selling the same article for Rs. $1,280$. At what price should the article be sold to make $25\%$ profit?

• A. Rs $2,000$
• B. Rs $2,200$
• C. Rs $2,400$
• D. Data inadequate

Answer 1

We know that, Profit $\% = \left(\dfrac{SP1 – CP}{CP}\right) \times 100\% $

Loss $\% = \left(\dfrac{CP – SP2}{CP}\right) \times 100\% $

given that$,\left(\dfrac{SP1– CP}{CP}\right) \times 100\% = \left(\dfrac{CP – SP2}{CP}\right) \times 100\%$

$\implies SP1 – CP = CP – SP2$

$\implies 2CP = SP1 + SP2$

$\implies 2CP = 1920+1280 = 3200$

$\implies CP = 1600$

Now,  Profit $\% =  25\%$

$\implies \left(\dfrac{SP – CP}{CP}\right) \times 100\% = 25\% $

$\implies (SP – 1600) \times 4 = 1600$

$\implies SP – 1600 = 800$

$\implies SP = Rs.\;2000$

So, the correct answer is $(A).$

Answer 2

Answer is A

Given statements

$\frac{100+P}{100} *CP=1920 ----(1)$                      $\frac{100-L}{100} *CP=1280 ----(2)$

$\frac{(1)}{(2)}$ ==> $\frac{100+P}{100-L} = \frac{1920}{1280}$

Since, % profit earned and % loss incurred are same[equate to x], $\frac{100+x}{100-x}=\frac{1920}{1280}$

On solving above equation, we will get P = L = 20%

Putting value of P in equation (1), we will get CP = Rs.1600

In order to make 25% profit, article should be sold at $\frac{1600*125}{100}=Rs.2000$