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A person sells a chair at a loss of 10%. If he had sold it at a profit of 5%, he would have earned 75 . What is the c.p of the chair.

Why this is not working

5=75/c.p  x100.

2 Answers

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Consider the following solution.

Let the C.P. of the chair be Rs 100. Then if it is sold at a profit of 5%, the SP becomes Rs 105. If it is sold at a loss of 10%, then S.P. becomes Rs 90. Difference between the two S.P. is as under:

105-90=Rs 15.

If the difference is Rs 15 then C.P.=Rs 100. Then for 1 chair, CP will be , 100/15. Then for Rs 75 100*75/15=Rs 500.

Hence the C.P. is Rs 500
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5 = 75 / C.P. x 100 will not work because 75 is not net profit (i.e.  S.P. - C.P.)
If 75 is considered as a profit, then using formula S.P. = C.P. + (P%) x C.P,  it will lead to C.P. = 1500.
Here, earning is difference between two transactions, with 10 % loss and 5 % profit.
Therefore,  75 = (S.P. with 5 % profit) - (S.P. with 10% loss)
75 = (C.P. + 0.05 x C.P.) - (C.P. - 0.1 x C.P.)
75 = (1.05 x C.P.) - (0.9 x C.P.)
75 = 0.15 x C.P.
C.P. = 500

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