The percentage profit earned by selling a table lamp for ₹214 is equal to the percentage loss incurred by selling the same table lamp for ₹146. At what price (in ₹) should the table lamp be sold to make 55% profit?​

Correct option is C

Given:

The percentage profit earned by selling the table lamp for ₹214 is equal to the percentage loss incurred by selling it for ₹146.

Concept Used:

When the percentage profit on one selling price is equal to the percentage loss on another selling price for the same article, the cost price (CP) can be found by taking the average of the two selling prices.

Formula Used:

Cost Price (CP) = $$\frac{\text{SP1} + \text{SP2}}{2}$$​​

Where SP1 = selling price for profit and SP2 = selling price for loss

SP = \text{CP} \times \left(1 + \frac{\text{Profit}\%}{100}\right)

Solution:

CP = $$\frac{214 + 146}{2} = \frac{360}{2}$$​ = ₹180

Thus, the cost price of the table lamp is ₹180

Selling Price for 55% Profit = $$180 \times \left(1 + \frac{55}{100}\right)$$​​

= $$180 \times 1.55$$​ = ₹279

The table lamp should be sold for ₹279 to make a 55% profit