A person incurs a 15% loss by selling an article for ₹170. At what price should the article be sold to earn a 10% profit?

Correct option is C

Given:

The person incurs a 15% loss by selling an article for ₹170.

We need to find the price at which the article should be sold to earn a 10% profit.

Concept Used:

Selling price SP = Cost Price − Loss for a loss, and

Selling price SP = Cost Price + Profit for a profit.

Solution:

Let the cost price of the article be C.

The person incurs a 15% loss, so the selling price of ₹170 is 85% of the cost price.

170 =$$C - \frac{15}{100} \times C = \frac{85}{100} \times C$$​

C =$$\frac{170 \times 100}{85} = \frac{17000}{85} = 200$$​

Therefore, the cost price C = ₹200.

To earn a 10% profit, the selling price should be 110% of the cost price:

SP = 20$$0 + \frac{10}{100} \times 200 = 200 + 20 = 220$$​

Thus, the article should be sold for ₹220 to earn a 10% profit.

Alternate Method:

Loss 15% = $$\frac3{20}$$

CP           :                 SP

20            :                 17

CP = $$\frac{170}{17}\times 20$$ = 200

To earn a 10% profit,

​SP = 200$$\times \frac {110}{100}$$ = 220​