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प्रश्न
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.
उत्तर
\[\text { Let C . P be Rs x and M . P be Rs y } . \]
\[\text { Gain% } = 50\]
\[\text { We know that }, \]
\[\text { S . P } = \left[ \frac{\left( 100 + \text { Gain % }\right)}{100} \times \text { C . P } \right]\]
\[ = \left[ \frac{150}{100} \times x \right]\]
\[ = \frac{3}{2}x\]
\[\text { Discount % } = 25\]
\[\text { Discount = 25 % of y }\]
\[ = Rs 0 . 25y\]
\[\text { So, S . P = M . P - Discount }\]
\[ = y - 0 . 25y\]
\[ = 0 . 75y\]
\[\text { So, S . P = 0 }. 75y\]
\[\text { Also, S . P = }\frac{3}{2}x\]
\[\text { Comparing both values for S.P., we get: }\]
\[\frac{3}{2}x = 0 . 75y\]
\[\frac{x}{y} = \frac{0 . 75 \times 2}{3}\]
\[ = \frac{1 . 5}{3}\]
\[ = \frac{1}{2}\]
\[\text { Thus, C . P: M . P } = 1: 2\]
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