A man sold a bicycle at 5% profit. If the cost had been 30% less and the selling price Rs.63 less, he would have made a profit of 30%. What was the cost price of the bicycle ?

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Solution

Let C.P. of the bicycle = Rs. 100
In the I case :
When Profit = 5%;
S.P. = Rs. (100+5) = Rs.105
In the II case :
C.P.= $(100 - \frac{30}{100} \times 100)$
= Rs. (100 - 30) = Rs. 70
Profit = 30%
S.P. = $\frac{(100 + P r o f i t)}{100} \times C . P .$
= $\frac{(100 + 30)}{100} \times R s .70 = \frac{130}{100} \times R s .70$
= Rs. $\frac{130 \times 70}{100} = R s . 91$
Difference of two selling prices
= Rs. 105-Rs.91 = Rs.14
If difference is Rs. 14 then C.P. of the bicycle
= Rs. 100
Re.1 = Rs. $\frac{100}{14}$
Rs.63 = Rs. $\frac{100}{14} \times 63$
= Rs. $\frac{100 \times 63}{14} = R s . 50 \times 9 = R s . 450$

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