Question

A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs 36.75 less, he would have gained 30%. Find the cost price of the article.

Answer 1

\[\text { Let the C . P of the article be Rs . x  }. \]

\[\text { Original S . P = x } + \frac{25}{100}x\]

\[ = Rs . \frac{5x}{4}\]

\[\text { If he purchased it at 20 % less }, \]

\[\text { C . P = x } - \frac{20}{100}x\]

\[ = \text {Rs} . \frac{4x}{5}\]

\[\text { He sold the article at Rs 36 . 75 less } . \]

\[\text { So, the selling price = Rs }. \frac{5x}{4} - 36 . 75\]

\[\text { Given that he would have gained 30 % selling at that price } . \]

\[\text { Therefore, gain % } = \frac{S . P - C . P}{C . P} \times 100\]

\[S . P - C . P = \frac{5x}{4} - 36 . 75 - \frac{4x}{5}\]

\[ = \frac{5x}{4} - \frac{4x}{5} - 36 . 75\]

\[ = \frac{25x - 16x}{20} - 36 . 75\]

\[ = \frac{9x}{20} - 36 . 75\]

\[\text { So, gain % } = \frac{S . P - C . P}{C . P} \times 100\]

\[30 = \frac{\frac{9x}{20} - 36 . 75}{\frac{4x}{5}} \times 100\]

\[ = \left( \frac{9x}{20} - 36 . 75 \right) \times \frac{5}{4x} \times 100\]

\[ = \frac{9x - 735}{16x} \times 100\]

\[30 = \frac{9x - 735}{16x} \times 100\]

\[\frac{225x - 18375}{4x} = 30\]

\[225x - 18375 = 120x\]

\[105x = 18375\]

\[x = \frac{18375}{105}\]

\[ = 175\]

\[\text { So, the cost price of the article is Rs . 175 } .\]