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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?

1. Rs $2,000$
2. Rs $2,200$
3. Rs $2,400$

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 $(A).$
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