Question

A dealer purchased 250 bulbs for ₹ 10 each. However, 12 bulbs got fused which he had to throw away. He sold the remaining bulbs at ₹ 12 each. Find the gain or loss per cent in the dealing.​

Answer 1

Given : A dealer purchased 250 bulbs for ₹ 10 each , However, 12 bulbs got fused which he had to throw away. He sold the remaining bulbs at ₹ 12 each.

Exigency To Find : The gain or loss percentage in the dealing ?

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⠀⠀⠀⠀¤ ⠀Finding Cost of 250 bulb when he purchased at ₹ 10 each :

⠀⠀▪︎⠀The dealer bought 250 bulb at ₹ 10 each .

$\qquad:\implies \sf \: Cost_{( \:\:250 \: bulbs \:\:)}\:=\: 10 \times 250 \:\:$

$\qquad:\implies \sf \: Cost_{( \:\:250 \: bulbs \:\:)}\:=\: 2500 \:\:$

$\qquad \therefore \pmb{\underline{\purple{\frak{\:\:Cost_{( \:\:250 \: bulbs \:\:)}\:=\: Rs.\: 2500 \:\:\: }}} }\bigstar$

The Cost of 250 bulbs that is purchased by dealer is ₹ 2500 .

Now ,

⠀⠀⠀⠀⠀⠀⠀☆ 12 bulbs got fused which he had to throw away and the remaining bulbs He sold at ₹ 12 each.

The 12 got fused from 250 bulbs , Therefore the no. of remaining bulbs are :

$\qquad \leadsto \sf \: Remaining_{(\:Bulbs\:)}\:=\: 250 - 12 \:$

$\qquad \leadsto \sf \: Remaining_{(\:Bulbs\:)}\:=\: 238 \:$

$\qquad \therefore \pmb{\underline{\purple{\frak{\:\: Remaining_{(\:Bulbs\:)}\:=\: 238 \:\:\:\: }}} }\bigstar$

The number of remaining bulbs is 238 .

⠀⠀⠀⠀⠀⠀⠀⠀⠀As , Per the Question , The Dealer sold the remaining bulbs at ₹ 12 each.

⠀⠀⠀⠀⠀¤ Finding Cost of 238 remaining bulb which he sold at ₹ 12 each :

⠀⠀▪︎⠀The dealer sold 238 remaining bulb at ₹ 12 each .

$\qquad:\implies \sf \: Cost_{( \:\:remaining \: bulbs \:\:)}\:=\: 12 \times 238 \:\:$

$\qquad:\implies \sf \: Cost_{( \:\:remaining \: bulbs \:\:)}\:=\: 2856 \:\:$

$\qquad \therefore \pmb{\underline{\purple{\frak{\:\:Cost_{( \:\:remaining \: bulbs \:\:)}\:=\: Rs.\: 2856 \:\:\: }}} }\bigstar$

The Cost of 238 remaining bulbs that is sold by dealer is ₹ 2856 .

$\qquad \leadsto \: \sf Cost \: Price \:=\: Rs.2500$

$\qquad \leadsto \: \sf Selling \: Price \:=\: Rs.2856$

Here the Selling Price is greater than Cost Price .

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Therefore , Dealer has made PROFIT in dealing .

⠀⠀⠀⠀⠀¤ Finding Profit Price :

$\qquad \dashrightarrow \sf Profit \: Price \: =\: Selling \:Price \:-\: Cost \:Price \:$

$\qquad \dashrightarrow \sf Profit \: Price \: =\: 2856 \:-\: 2500 \:$

$\qquad \dashrightarrow \sf Profit \: Price \: =\: 356 \:$

$\qquad \therefore \pmb{\underline{\purple{\frak{\:\:Profit \:Price\:=\: Rs.\: 356 \:\:\: }}} }\bigstar$

The Profit Price is ₹ 356 .

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀¤ Finding Profit Percentage ( % ) :

$\dag\:\:\pmb{ As,\:We\:know\:that\::}\\\\\qquad\maltese\: \bf Formula\: for \: Profit\:Percentage \:\:(\% )\::$

$\qquad \dag\:\:\bigg\lgroup \pmb{\frak{ Profit \:\% \: \:= \dfrac{ Profit \: Price }{ Cost \: Price}\times 100 }}\bigg\rgroup$

⠀⠀⠀⠀Here , the Profit Price is ₹ 356 & Cost Price is ₹ 2500

$\qquad \dashrightarrow \sf Profit \:\% \: \:= \dfrac{ Profit \: Price }{ Cost \: Price}\times 100 \:$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \dashrightarrow \sf Profit \:\% \: \:= \dfrac{ Profit \: Price }{ Cost \: Price}\times 100 \:$

$\qquad \dashrightarrow \sf Profit \:\% \: \:= \dfrac{ 356 }{ 2500 }\times 100 \:$

$\qquad \dashrightarrow \sf Profit \:\% \: \:= \dfrac{ 356 }{ \cancel {2500} }\times \cancel {100} \:$

$\qquad \dashrightarrow \sf Profit \:\% \: \:= \dfrac{ 356 }{ 25} \:$

$\qquad \dashrightarrow \sf Profit \:\% \: \:= 14.24 \:$

$\qquad \therefore \pmb{\underline{\purple{\frak{\:\:Profit \:\% \: \:= 14.24 \:\%\:\: }}} }\bigstar$

Hence , Profit Percentage made by dealer in dealing is 14.24 %