# The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make a 25% profit?

A. Rs. 2000
B. Rs. 2200
C. Rs. 2400
D. Rs. 2600

The correct answer is “Rs. 2000”.
Step by Step Solution:
suppose the cost price of the product is Rs. X
Remember these formulas for Profit % and Loss %

\text { profit) } \%=\frac{\text { selling price }-\cos t \text { price }}{\cos t \text { price }} \times 100

(\text { loss }) \%=\frac{\cos t \text { price }-\text { selling price }}{\cos t \text { price }} \times 100

According to the problem statement, the percentage profit is equal to the percentage loss incurred.

Profit % = Loss %

\frac{\text { selling price }-\cos t \text { price }}{\cos t \text { price }} \times 100 = \frac{\cos t \text { price }-\text { selling price }}{\cos t \text { price }} \times 100

\frac{1920-x}{x} \times 100=\frac{x-1280}{x} \times 100

“X and 100” on both sides of the equation will cancel each other.
then we will have
⇒ 1920−x = x−1280
⇒ 2x = 3200
⇒ x = 1600
Now, for-profit of 25%
we will use this formula

Profit% =\frac{\text { (selling price – cost price) }}{\text { cost price }} \times 100

25 =\frac{\text { (selling price – 1600) }}{\text { 1600 }} \times 100

\frac{25\times1600}{100} = Selling price – 1600

400 = Selling price – 1600
Selling price to gain 25% = 400+1600
Selling price to gain 25% = 2000

So the article should be sold at 2000 to make a 25% profit.
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