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 is the cost price of the bicycle ?

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Solution

For the first situation,
Profit % $= \frac{S . P . - C . P .}{C . P .} \times 100 = 5$
$=> S . P . - C . P . = 0.05 C . P .$
$=> S . P . = 1.05 C . P$ --- (1)
For the second situation, Selling price $=$ Selling price of 1st situation $- R s 63$
And Cost price is $30$ % less or $= 70$ % of C.P. $= 0.7 C . P .$
So, Profit % $= \frac{S . P . - C . P .}{C . P .} \times 100 = 30$

$=> \frac{(S . P . - 63) - 0.7 C . P .}{0.7 C . P .} \times 100 = 30$

$=> S . P . - 63 - 0.7 C . P . = 0.21 C . P .$
$=> S . P . = 0.91 C . P + 63$ --- (2)
From, equations 1, 2
$1.05 C . P . = 0.91 C . P + 63$
$=> 0.14 C . P . = 63$
$C . P . = R s 450$
Thus, cost price of the bicycle $= R s 450$

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