Question

A shopkeeper sold an item at 20% profit. If he had bought the same item at 20% less cost, he would have had 25% profit even after cutting down its selling price by ₹100. What is the cost price of the item?

Answer 1

Answer:

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Answer 2

$\huge\mathcal{\mid{\mid{\underline{\purple{Good\: Afternoon\:}}}{\mid{\mid}}}}$

$\huge{\orange{\boxed{\fcolorbox{lime}{black}{\red{QUESTION}}}}}$

☘️ A shopkeeper sold an item at 20% profit. If he had bought the same item at 20% less cost, he would have had 25% profit even after cutting down its selling price by ₹100. What is the cost price of the item?

$\huge{\orange{\boxed{\fcolorbox{lime}{indigo}{\color{aqua}ANSWER}}}}$

$\Large\bf{\color{cyan}Let,}$

• $\bf{\red{Cost\: price}}\:=\:x\:$

$\Large\bf\pink{GiVeN,}$

• $\bf{\red{Profit}}\:=\:20\%\:$

$\bf\purple{We\: know\:that,}$

$\orange\bigstar\:\:\bf\blue{S.P\:=\:C.P\:+\: Profit}$

$\longmapsto\:\:\bf{S.P\:=\:x\:+\:\dfrac{x\times{20}}{100}\:}$

$\longmapsto\:\:\bf{S.P\:=\:x\:+\:\dfrac{x}{5}\:}$

$\longmapsto\:\:\bf{S.P\:=\:\dfrac{6x}{5}\:}$

$\Large\bf\green{Now,}$

$:\implies\:\:\bf{New\:C.P\:=\:x\:-\:x\times{\dfrac{20}{100}}\:}$

$:\implies\:\:\bf{New\:C.P\:=\:x\:-\:{\dfrac{x}{5}}\:}$

$:\implies\:\:\bf{New\:C.P\:=\:{\dfrac{4x}{5}}\:}$

$\Large\bf\red{And,}$

$:\implies\:\:\bf{New\:S.P\:=\:\dfrac{6x}{5}\:-\:100}$

$\Large\bf\red{And,}$

$:\implies\:\:\bf{Profit\:=\:\dfrac{6x}{5}\:-\:100\:-\:\dfrac{4x}{5}\:}$

$:\implies\:\:\bf{Profit\:=\:\dfrac{2x}{5}\:-\:100\:}$

$:\implies\:\:\bf\purple{\%{Profit}\:=\:\dfrac{\frac{2x}{5}\:-\:100}{\frac{4x}{5}}\times{100}\:}$

$:\implies\:\:\bf{25\:=\:\Big(\dfrac{\frac{2x}{5}}{\frac{4x}{5}}\:-\:\dfrac{100}{\frac{4x}{5}}\Big)\times{100}\:}$

$:\implies\:\:\bf{25\:=\:\Big(\dfrac{1}{2}\:-\:\dfrac{125}{x}\Big)\times{100}\:}$

$:\implies\:\:\bf{25\:=\:\dfrac{1}{2}\times{100}\:-\:\dfrac{125}{x}\times{100}\:}$

$:\implies\:\:\bf{25\:=\:50\:-\:\dfrac{125}{x}\times{100}\:}$

$:\implies\:\:\bf{\dfrac{125}{x}\times{100}\:=\:50\:-\:25\:}$

$:\implies\:\:\bf{\dfrac{125}{x}\times{100}\:=\:25\:}$

$:\implies\:\:\bf{x\:=\:\dfrac{125\times{100}}{25}}$

$:\implies\:\:\bf{x\:=\:5\times{100}}$

$:\implies\:\:\bf\green{x\:=\:Rs.500}$