Question

a person sold an article at a profit of 20% . if he sold it for Rs 81 less , his loss ,his loss would have been 12% find the cp of the article?

Answer 1

$\huge {\bold {\underline {\underline{Given : - }}}}$

• A person sold an article at a profit of 20%
• Loss% When the same article was sold Rs.81 less is 12%

$\huge {\bold {\underline {\underline{To \: find: - }}}}$

• Cost price of the article

$\huge {\bold {\underline {\underline{Solution: - }}}}$

Let Selling price when the article is sold at a profit of 20% be (SP)

Cost price of the article be (CP)

Profit% of an article is given by ,

$\large{\sf{\underline {\bold {\boxed {\bigstar{ | \: Profit\% = \dfrac{(SP - CP )100}{ CP} }}}}}}$

We are given that profit% = 20%

$: \sf\implies \: 20 = \dfrac{(SP - CP)100}{ CP} \\ \\ \sf :\implies \: 20CP = 100(SP - CP) \\ \\ \sf :\implies \: 20CP = 100SP - 100CP \\ \\ \sf : \implies \: 20CP + 100CP = 100SP \\ \\ \sf :\implies \: 120CP = 100SP \\ \\ \sf: \implies \: CP = \dfrac{ \cancel{100}SP}{ \cancel{120}} \\ \\ : \implies {\bold {\boxed {\pink {CP = \dfrac{5SP}{6} }}}} \rightarrow \: eq(1)$

Loss% when the article is sold for Rs.81 less than in case-I is 12%

Loss% of an article is given by,

$\large {\sf {\underline {\bold {\boxed {\bigstar{ \: | \: loss\% = \dfrac{(CP - SP)100}{CP} }}}}}}$

We have ,

In first case SP = (SP) then Rs.81 less than in first case is nothing but (SP-81) becomes the SP of the article in second case.

• SP in second case = (SP - 81)
• Loss% = 12%
• CP is constant

$\sf \\ \sf: \implies \: 12 = \dfrac{[ CP - (SP - 81 ) ]100}{CP} \\ \\ \sf : \implies \: 12CP = [ CP - (SP - 81 ) ]100 \\ \\ \sf : \implies \: 12 \bigg( \dfrac{5SP}{6} \bigg) = \bigg[ \bigg( \dfrac{5SP}{6} \bigg) - (SP - 81 ) \bigg] 100\\ \\ \sf: \implies \: \dfrac{60SP}{6} = \bigg[ \dfrac{5SP - 6(SP - 81)}{6} \bigg ]100 \\ \\ \sf : \implies \: \dfrac{ \cancel{60}SP}{ \cancel{6}} = \bigg[ \dfrac{(5SP - 6SP + 486)100}{6} \bigg ] \\ \\ \sf : \implies \: (10SP)(6) = (486 - SP)100 \\ \\ \sf : \implies \: 60SP = 48600 - 100SP \\ \\ \sf : \implies \: 60SP + 100SP = 48600 \\ \\ \sf : \implies \: 160SP = 48600 \\ \\ \sf : \implies \: SP = \dfrac{48600}{160} \\ \\ \sf : \implies \: SP = Rs \: 303.75$

From eq(1) ,

$\sf \: CP = \dfrac{5SP}{6} \\ \\ : \sf\implies \: CP = \dfrac{5(303.75)}{6} \\ \\ \sf: \implies \: CP =Rs \: 253.125$

∴ The cost price of the Article is Rs 253.125