Question

A man sells a bicycle at a profit of 25% Had he bought it at a price less by 25% and sold it at Rs 250 less then also he could have made a profit of 25% .Find the cost price of the bicycle.​

Answer 1

Step-by-step explanation:

Given:-

• A man sells a bicycle at a profit of 25%

• If he had bought it at a price less by 25% and sold it at Rs 250 less, he had made a profit of 25%.

To Find:-

• The cost price of the bicycle.

Solution:-

Let the CP of the bicycle be x

Profit% = 25%

$\sf \implies SP = \dfrac{100 +Profit\%}{100} \times CP$

$\sf \implies SP = \dfrac{100 +25}{100} \times x$

$\sf \implies SP = \dfrac{125x}{100}$

$\sf \underline{If \: the \: CP \: is \: 25\% \: less:-}$

$\sf New \: CP = x - 25\% \: of \: x$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = x - \dfrac{25x}{100}$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{100x - 25x}{100}$

$\sf \therefore New \: CP = \dfrac{75x}{100}$

$\sf Profit\% = 25\%$

$\sf New \: SP = \dfrac{100 +Profit\%}{100} \times New\: CP$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{100 +25}{100} \times \dfrac{75x}{100}$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{9375x}{10000}$

$\sf The \: SP\: would \: be \: Rs.250 \: less$

$\sf \implies \dfrac{125x}{100} - \dfrac{9375x}{10000} = 250$

$\sf \implies \dfrac{12500x - 9375x}{10000} = 250$

$\sf \implies \dfrac{3125x}{10000} = 250$

$\sf \implies 3125x = 2500000$

$\sf \implies x = \dfrac{2500000}{3125}$

$\sf \implies x = 800$

$\underline{\boxed{\therefore \textsf{\textbf{ Cost \: price \: of \: the \: bicycle = Rs.800}}}}$