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Question

A bicycle is sold at a gain of $$16\%$$. Had it been sold $$Rs 100$$ more, the gain would have been $$20\%$$. Find the $$C.P$$ of the bicyle.


Solution

Let cost price $$= C.P \,\, and \,\, Selling \, price = S.P$$
$$\Rightarrow Gain $$% $$= \frac {S.P-C.P}{C.P}\times 100 \Rightarrow  \frac {16}{100}=\frac {S.P-C.P}{C.P}\Rightarrow \frac {SP}{CP}=\frac {116}{100}$$
and $$ \frac {20}{100}=\frac {S.P +100-C.P}{C.P} \Rightarrow  \frac {1}{5}=\frac {SP}{CP}+\frac {100}{CP}-1$$
$$\Rightarrow  \frac {6}{5}=\frac {116}{100} +\frac {100}{CP} \rightarrow \frac {100}{C}=\frac {6}{5}-\frac {58}{50}=\frac {300-290}{250}=\frac {10}{250}$$
$$\Rightarrow CP=\frac {100\times 250}{10}= Rs.\, 2500$$ 

Mathematics

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