Question

A shopkeeper marks his goods at such a price that after allowing a discount of 25% on the marked price, he still makes a profit of 50% find the ratio of the CP to the MP. ​

Answer 1

Answer:

CP : MP = 1 : 2

Step-by-step explanation:

Let the cost price be 100.

Given, Gain = 50%.

Selling price = 100 + 50 = 150.

Given, discount = 25%.

Marked price = (150 * 100)/75

                      = 200.

⇒ (CP/MP) = 100/200

∴ CP : MP = 1 : 2

Hope it helps!

Answer 2

Answer:

$\texttt{Ratio of CP to MP = 1 : 2}$

Step-by-step explanation:

$\texttt {Let the C.P be Rs. x}$

$\texttt {Let the M.P be Rs. y}$

$\tt {Gain \% = 50\%}$

$\tt{S.P = {\frac {CP ( 100 + P\% )}{100}}}$

$\tt{\implies S.P = {\frac {150x }{100}}}$

$\tt{\implies S.P = {\frac {3x }{2}}}$

$\tt{Discount \% = 25\%}$

$\tt{Discount = {\frac {Discount \times MP}{100}}}$

$\tt{\implies Discount = {\frac {25 \times y}{100}}}$

$\tt{\implies Discount = {\frac {25y}{100}}}$

$\tt{\implies Discount = Rs. 0.25y}$

$\texttt{S.P = M.P – discount}$

$\texttt{\implies S.P = 0.75 y}$

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

$\texttt{Comparing both the values for S.P we get,}$

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

$\texttt {1.5x = 0.75 y}$

$\texttt {1.5x = 0.75 y}$

$\tt {\frac {x }{y} = \frac {0.75}{1.5}}$

$\tt {\frac {x }{y} = \frac {75}{150}}$

$\tt {\frac {x }{y} = \frac {1}{2}}$

$\tt{\underline{\therefore \: Ratio \: of \: CP \: to \: MP = 1 : 2}}$