A shopkeeper marks his goods in such a way that after allowing a discount of 25% on the marked price,
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.

Solution:

Let C.P be Rs $x$ and M.P be Rs $y$.

Gain $\%=50$

We know that,

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

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

$=\frac{3}{2} x$

Discount $\%=25$

Discount $=25 \%$ of $y$

$=$ Rs $0.25 y$

So, S.P = M.P – Discount

$=y-0.25 y$

$=0.75 y$

So, S.P $=0.75 y$

Also, S.P $=\frac{3}{2} x$

Comparing both values for S.P., we get:

$\frac{3}{2} x=0.75 y$

$\frac{x}{y}=\frac{0.75 \times 2}{3}$

$=\frac{1.5}{3}$

$=\frac{1}{2}$

Thus, C.P : M.P = $1: 2$