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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%. Find the cost price of rack sold at 10% loss.  


1. Rs. 4,000
2. Rs. 3,200
3. Rs. 5,000
4. Rs. 3,520

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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.

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