Question

A shopkeeper marks his goods in such a way that after allowing a discount of 25% on the marked price, he still makes a profit of 50%. Find the ratio of the C.P. to the M.P.

Answer 1

\[\text { Let C . P be Rs x and M . P be Rs y } . \]

\[\text { Gain% } = 50\]

\[\text { We know that }, \]

\[\text { S . P } = \left[ \frac{\left( 100 + \text { Gain %  }\right)}{100} \times \text { C . P } \right]\]

\[ = \left[ \frac{150}{100} \times x \right]\]

\[ = \frac{3}{2}x\]

\[\text { Discount % } = 25\]

\[\text { Discount = 25 % of y  }\]

\[ = Rs 0 . 25y\]

\[\text { So, S . P = M . P - Discount }\]

\[ = y - 0 . 25y\]

\[ = 0 . 75y\]

\[\text { So, S . P = 0  }. 75y\]

\[\text { Also, S . P =  }\frac{3}{2}x\]

\[\text { Comparing both values for S.P., we get: }\]

\[\frac{3}{2}x = 0 . 75y\]

\[\frac{x}{y} = \frac{0 . 75 \times 2}{3}\]

\[ = \frac{1 . 5}{3}\]

\[ = \frac{1}{2}\]

\[\text { Thus, C . P: M . P } = 1: 2\]