Ramesh bought 2 boxes for Rs. 1300. He sold one box at a profit of 20% and the other at a loss of 12%. If the selling price of both the boxes is the same. Find the cost of each box.

A profit or loss is the difference between the cost price and the selling price. If the cost price is more than the selling price, then the transaction results in a loss, whereas if the selling price is more than the cost price then the transaction results in a profit.

Answer: The cost price of the  first box and the second box where the 2 boxes are bought for Rs.1300, the first one sold at a profit of 20% and the other at a loss of 12% with their selling price to be the same are Rs 550 and Rs 750 respectively

A profit% or loss% is calculated always on the cost price, that is Profit% or Loss% = (Profit or Loss)/CP × 100

Explanation:

Let the cost price of the first box be 'x' and then the cost price of the second box will be '(1300 - x)'.

Let the selling price of the first box be \((SP)_{1}\), since the first box is sold at 20% profit, therefore:

Profit% = (SP - CP)/CP × 100

or, 20 = (\((SP)_{1}\) - x)/x × 100

or, 20/100 = (\((SP)_{1}\) - x)/x

or, 20x =  100 × ( \((SP)_{1}\) - x)

or, 20x =  100 \((SP)_{1}\) - 100x

or, 100 \((SP)_{1}\) = 100x + 20x

or, 100 \((SP)_{1}\) = 120x

or, \((SP)_{1}\) = 120x/100 ---------------------- (1)

Let the selling price of the table be \((SP)_{2}\), since the second box is sold at 12% loss, therefore:

Loss % = (CP - SP)/CP × 100

or, 12 = ((1300 - x - \((SP)_{2}\))/(1300 - x))× 100

or, 12/100 = ((1300 - x - \((SP)_{2}\))/(1300 - x))

or, 12 × (1300 - x) = 100 × (1300 - x - \((SP)_{2}\))

or, 15600 - 12x = 130000 - 100x - 100\((SP)_{2}\)

or, 100\((SP)_{2}\) =  130000 - 100x - 15600 + 12x

or, 100\((SP)_{2}\) = 114400 - 88x

or, \((SP)_{2}\) = (114400 - 88x)/100 ----------------------- (2)

Since the the selling price of both of the boxes are same, we have:

\((SP)_{1}\) = \((SP)_{2}\)

Thus, equating equation(1) and equation(2) we get,

120x/100 = (114400 - 88x)/100 

or,120x = 114400 - 88x

or, 120x + 88x = 114400

or, 208x = 114400

or, x = 114400/208 = 550

So, the cost price of the first box is = x = Rs 550

Cost price of the second box is = 1300 - x = 1300 - 550 = Rs 750

Therefore, the cost price of both the boxes are Rs 550 and Rs 750 respectively.