Question

How much percent more than C.P should a manufacturer mark his goods so that after allowing discount of 20% on marked price,he gains 10%? ​

Answer 1

Solution :

Let the Cost price be Rs 100

Gain percent required = 10%

$\therefore$ S.P = Rs(100+10) = Rs 110

Discount allowed = 20%

Let the Marked Price be x. Then,

$\sf \: Discount = 20\% \: of \: x$

$\hookrightarrow \sf \: (\dfrac{20}{100} \times x) = Rs \: \dfrac{x}{5}$

$\boxed{\rm \: S.P = M.P - Discount}$

$\hookrightarrow \sf \: Rs (x - \dfrac{x}{5} ) = Rs \: \dfrac{4x}{5}$

But,S.P = Rs 110

$\therefore \sf \: \dfrac{4x}{5} = 110$

$\hookrightarrow \sf \: x = \dfrac{550}{4}$

$\sf \: x = \large \boxed{ \sf Rs \: 137.50}$

Hence,the manufacturer should mark 37.50% more than C.P

Aliter :

Let the C.P be Rs x

Gain = 10%

$\boxed{\rm \: S.P = ( \dfrac{100 + Gain\%}{100} ) \times C.P}$

$\hookrightarrow \sf \: S.P = Rs( \dfrac{100 + 10}{100} \times x)$

$\hookrightarrow \sf \: S.P = Rs \: \dfrac{11x}{10}$

Now,

S.P. = Rs 11x/10

Discount = 20%

$\sf \: \boxed { \rm \: \: M.P = \dfrac{100 \times S.P}{100 -Discount } }$

$\hookrightarrow \sf \: M.P = Rs \: ( \dfrac{100 \times \dfrac{11x}{10} }{100 - 20} )$

$\hookrightarrow \sf \: M.P = Rs \: \dfrac{11x}{8}$

$\boxed{ \rm \: Req. \: \% = \frac{M.P - C.P}{C.P} \times 100}$

$\hookrightarrow \sf \: \dfrac{ \dfrac{11x}{8} - x}{x} \times 100$

$\hookrightarrow \sf \: \dfrac{3}{8} \times 100$

$= \large \boxed{ \sf \: 37.5\%}$

Answer 2

$\bf{\Huge{\boxed{\rm{\green{ANSWER\::}}}}}$

$\bf{\Large{\underline{\bf{Given\::}}}}$

A manufacturer mark his goods so that after allowing discount of 20% on marked price, he gains 10%.

$\bf{\Large{\underline{\bf{To\:find\::}}}}}$

The percent more than C.P.

$\bf{\Large{\underline{\rm{\pink{Explanation\::}}}}}$

We know that formula of the marked Price,[M.P.]

$\leadsto\sf{\orange{M.P.\:=\:\frac{100*S.P.}{100-discount\%}} }$

Let the Cost Price,[C.P.] be Rs.100

Therefore,

$\longmapsto\tt{Selling\:price,[S.P.]\:=\:C.P.*(\frac{100+gain\%}{100} )}$

$\longmapsto\tt{S.P.\:=\:100*(\frac{100+10}{100}) }$

$\longmapsto\tt{S.P.\:=\:100*\frac{110}{100} }$

$\longmapsto\tt{S.P.\:=\:\cancel{100}*\frac{110}{\cancel{100}} }$

$\longmapsto\tt{\orange{S.P.\:=\:Rs.110}}$

Now,

$\leadsto\rm{Marked\:price,[M.P.]\:=\:\frac{100*S.P.}{100-Discount\%} }$

$\leadsto\rm{M.P.\:=\:\frac{100*110}{100-20} }$

$\leadsto\rm{M.P.\:=\:\cancel{\frac{11000}{80} }}$

$\leadsto\rm{\orange{M.P.\:=\:Rs.137.5}}$

______________________________________________

$\mapsto\sf{Above\%\:=\:\frac{M.P.-C.P.}{100} *100}$

$\mapsto\sf{Above\%\:=\:\frac{137.5-100}{100} *100}$

$\mapsto\sf{Above\%\:=\:\frac{137.5-100}{\cancel{100}} *\cancel{100}}$

$\mapsto\sf{Above\%\:=\:137.5\:-\:100}$

$\mapsto\sf{\orange{Above\%\:=\:37.5\%}}$