The cost price of an item A is Rs.400 more than that of B. Item A is sold at a loss of 10% and Item B is sold at a profit of 60%. If there is a profit of 20% in the entire transaction, then what is the selling price of item A?

Correct option is C

Given :

Loss on A = 10%
Profit on B = 60%
Overall profit = 20%

Formula Used :

Selling Price (SP) = Cost Price (CP) × (1 ± Profit/Loss %)

Overall Profit % =$$\dfrac{\text{Total SP − Total CP}}{\text{Total CP}} \times 100$$​​

Solution :

​Let the cost price of item B = ₹x

Then, cost price of item A = ₹(x + 400)

SP of A = (x + 40$$0) \times$$ 90% = 0.9(x + 400) 

SP of B = x$$\times$$​ 160% = 1.6x

Total CP = x + (x + 400) = 2x + 400 

Total SP = 0.9(x + 400) + 1.6x

Given overall profit = 20%
Total SP = 1.$$2 \times$$​ Total CP

0.9(x + 400) + 1.6x = 1.2(2x + 400)

0.9x + 360 + 1.6x = 2.4x + 480

2.5x + 360 = 2.4x + 480

0.1x = 120

x = 1200
Cost price of A = 1200 + 400 = 1600

SP of A = 90% of 1600 = ₹1440

Selling price of item A = ₹1440