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1. A sells an article to B at a profit of 10% B sells the article back to A at a loss of 10%. In this transaction:

A. A neither losses nor gains

B. A makes a profit of 11%

C. A makes a profit of 20%

D. B loses 20%

Solution:

First Method
Let CP was 100 for A originally
A sells article to B at 10% profit,
CP for B = 100 + 10% of 100 = 110
Now, B sells it A again with loss 10%
Now, CP for A this time = 110 - 10% of 110 = 99
A makes Profit = 110 - 99 = 11
%profit for A =

\frac{11 \times 100}{100}

= 11%

Second Method
It could be easily shown by net percentage change graphic.
100(A) == 10%(Profit) ⇒110(B) == 10%(Loss) ⇒ 99(A)

In this transaction A makes a profit of (110 - 99 = 11%) 11%

[10% on selling to B and 1% profit on buying back from B]

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