Question

Find the Cost price when : S.P. = rs 1500 and gain = 20%

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Answer 1

Answer:

$1500 = (100\% + 20\%) = 120\%$

$120\% = 1500 \\ 1\% = \frac{1500}{120} \\ 100\% = \frac{1500}{120} \times 100 = 1250$

$C.P.= Rs.1250$

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Answer 2

★ Required answer:-

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• The cost price is of ₹ 1250.

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$\qquad\qquad\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}$

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★ Given:-  

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• S.P. = Rs. 1500
• Gain% = 20%

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★ To find:-  

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• Cost price

★ Formula Used:-  

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$\qquad\dag\:\qquad\:\boxed{\sf{Gain\:\%\:=\:\dfrac{Sp\:-\:Cp}{Cp}\:\times\:100}}\:\qquad\:\dag$

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★ Solution:-    

$\qquad\qquad\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}$

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$\textsc{Let\:the\:cost\:price\:be\:=\:x}$

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$\qquad\sf{:\implies\:Gain\:\%\:=\:\left(\dfrac{Sp\:-\:Cp}{Cp}\:\right)\:\times\:100}$

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$\qquad\sf{:\implies20\:=\:\left(\:\dfrac{1500\:-\:x}{x}\:\right)\times\:100}$

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$\qquad\sf{:\implies\:20\:=\:\dfrac{150000\:-\:100\:x}{x}}$

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$\qquad\sf{:\implies\:20\:x\:=\:150000\:-\:100\:x}$

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$\qquad\sf{:\implies\:20\:x\:+\:100\:x\:=\:150000}$

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$\qquad\sf{:\implies\:120\:x\:=\:150000}$

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$\qquad\sf{:\implies\:x\:=\:\dfrac{150000}{120}}$

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$\qquad\sf{:\implies\:x\:=\:\dfrac{15000}{12}}$

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$\qquad\sf{:\implies\:x\:=\:1250}$

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$\underline{\underline{\textsc{\:Hence\:the\:cost\:price\:is\:of\:Rs.\:1250}}}$

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$\qquad\qquad\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}$