Correct Answer - Option 2 : Rs. 3,200
Given:
M made a no profit-no loss deal. He purchased two racks for Rs. 5,200.
One rack was sold at the gain of 16% while another rack was sold at the loss of 10%.
Concepts used:
Gain % = (Gains/C.P.) × 100
Loss % = (Loss/C.P.) × 100
Calculation:
M made a no profit-no loss deal. He purchased two racks for Rs. 5,200.
Let C.P. of one rack be Rs. x.
⇒ C.P. of another rack = 5,200 – x
One rack was sold at the gain of 16%.
⇒ 16 = {(S.P. – x)/x} × 100
⇒ S.P. of one rack = 29x/25
Another rack was sold at the loss of 10%.
⇒ 10 = (5,200 – x – S.P.)/(5,200 – x) × 100
⇒ S.P. for another rack = 4,680 – (9x/10)
M made a no profit-no loss deal.
⇒ Total S.P. = Total C.P.
⇒ 29x/25 + 4,680 – (9x/10) = 5,200
⇒ 29x/25 – (9x/10) = 5,200 – 4,680
⇒ x = Rs. 2,000
⇒ C.P. of rack sold at loss = 5,200 – 2,000 = Rs. 3,200
∴ Cost price of rack sold at loss is Rs. 3,200.
