Question

A buys an article and sells it to B at a profit of 12%. B sells it back to A at the price which A previously paid for it. what is B's percentage loss?

Answer 1

Let A's CP = Rs.k. Therefore A''s SP = B's CP = [(100+Profit%)/100]xCPof A
= (112/100)xk = 1.12k.
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B's CP = 1.12k,  B's  SP = A's CP = k.
==> B's loss = B's CP - B's SP = 1.12k - k = 0.12k.

B's loss percent = (B's loss/B's CP) x 100 = (0.12k / 1.12k) x 100 = 1200/112
= 10 5/7 % 

Answer 2

Let the Original C.P of the article(price at which A purchased it) be Rs.x
S.P. of the article=C.P.*(100+Profit%)/100=x*112/100=28x/25
which is equal to the C.P. of B(Price paid by B for the article)
S.P. of B=(Price at which A purchased it)=Rs.x
Loss of B=C.P.-S.P.
=28x/25-x
=3x/25
Loss percentage=Loss/C.P.*100
=(3x/25)/x*100%=12%
Hence B loses 12%