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 ?
For the first situation,
Profit % $$ = \dfrac {S.P. - C.P.}{C.P.} \times 100 =5 $$
$$ => S.P. - C.P. = 0.05 C.P. $$
$$ => S.P. = 1.05 C.P $$ --- (1)
For the second situation, Selling price $$ = $$ Selling price of 1st situation $$ - Rs 63 $$
And Cost price is $$ 30 $$ % less or $$ = 70 $$ % of C.P. $$ = 0.7 C.P. $$
So, Profit % $$ = \dfrac {S.P. - C.P.}{C.P.} \times 100 =30 $$
$$ => \dfrac {(S.P. -63) - 0.7C.P.}{0.7C.P.} \times 100 = 30 $$
$$ => S.P. -63 - 0.7C.P. = 0.21 C.P. $$
$$ => S.P. = 0.91 C.P + 63 $$ --- (2)
From, equations 1, 2
$$ 1.05 C.P. = 0.91C.P + 63 $$
$$ => 0.14C.P. = 63 $$
$$ C.P. = Rs 450 $$
Thus, cost price of the bicycle $$ = Rs 450 $$