Question

Anu earns a profit or 18% by selling an article at a certain price. If she were to sell it for 10.50 more, she would have gained 25%. The original cost price of 12 such
articles is​

Answer 1

$\sf\small\underline\purple{Let:-}$

$\tt{\leadsto Cost\: price\:_{(article)}=x}$

$\sf\small\underline\purple{To\:Find:-}$

$\tt{\leadsto Cost\: price\:_{(12\:article)}=?}$

$\sf\small\underline\purple{Solution:-}$

We will solve this question by applying formula. As per the given clue in the question.

$\sf\small\underline\pink{Given\:in\:case-(i):-}$

$\tt\small\underline{CP=x\:\:\:P=18\%:-}$

$\tt{\leadsto SP=\bigg(\dfrac{100+P\%}{100}\bigg)\times\:CP}$

$\tt{\leadsto SP=\bigg(\dfrac{100+18}{100}\bigg)\times\:x}$

$\tt{\leadsto SP=\bigg(\dfrac{118}{100}\bigg)\times\:x}$

$\tt{\leadsto SP=\bigg(\dfrac{118x}{100}\bigg)}$

$\tt{\leadsto SP=\dfrac{118x}{100}+10.50}$

$\sf\small\underline\pink{Given\:in\:case-(ii):-}$

$\tt\small\underline{CP=x\:\:\:P=25\%:-}$

$\tt{\leadsto SP=\bigg(\dfrac{100+P\%}{100}\bigg)\times\:CP}$

$\tt{\leadsto SP=\bigg(\dfrac{100+25}{100}\bigg)\times\:x}$

$\tt{\leadsto SP=\bigg(\dfrac{125}{100}\bigg)\times\:x}$

$\tt{\leadsto SP=\bigg(\dfrac{125x}{100}\bigg)}$

$\tt{\leadsto SP=\dfrac{125x}{100}}$

• $\sf{Cp\:of\: orginal\: article:-}$

$\tt{\leadsto SP\:_{(case-(ii))}=SP\:_{(case-(i))}}$

$\tt{\leadsto \dfrac{125x}{100}=\dfrac{118x}{100}+10.50}$

$\tt{\leadsto \dfrac{125x}{100}-\dfrac{118x}{100}=10.50}$

$\tt{\leadsto \dfrac{125x-118x}{100}=10.50}$

$\tt{\leadsto \dfrac{7x}{100}=10.50}$

$\tt{\leadsto 7x=1050}$

$\tt{\leadsto x=150}$

$\sf\large{Hence,}$

$\tt{\leadsto Cost\: price\:_{(12\:article)}=12x}$

$\tt{\leadsto Cost\: price\:_{(12\:article)}=12(150)}$

$\bf{\leadsto Cost\: price\:_{(12\:article)}=1800}$

Answer 2

Given :-

Anu earns a profit or 18% by selling an article at a certain price. If she were to sell it for 10.50 more, she would have gained 25%

To Find :-

Original cost price of 12 such  articles is​

Solution :-

Let the original cost price be a

We know that

SP = 100 + P%/100 × CP

SP = 100 + 18/100 × a

SP = 118/100a

Now

SP = 100 + P%/100 × CP

SP = 100 +  25/100 × a

SP = 125a/100

Now

125a/100 = 118a/100 + 10.5

125a/100 - 118a/100 = 10.5

125a - 118a/100 = 10.5

125a - 118a = 10.5 × 100

7a = 1050

a = 1050/7

a = 150

Cost price of 12 article = 12(150) = 1800

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