Question

A man buys an article at rs x and sells it at rs 750 and thereby he gains 25%. The value of x

Answer 1

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$\underline{\underline{\huge{\textbf{Solution:}}}}$

Given,
Cost Price of an Article = Rs. x
Selling Price of the Article = Rs. 750
$Gain\%$ = 25$\%$

$\underline{\large{\textbf{Step-1:}}}$
Find Estimated Value of Cost Price.

It is given that,
There is a Gain,

$\bigstar \textsf{When there is a Gain, Selling Price (SP) > Cost Price(CP)}$

$\implies x > 750$

Thus,
Cost Price of the Article will be Less than Rs. 750.

$\underline{\large{\textbf{Step-2:}}}$
Find the Gain

$\bigstar \textsf{Gain = Selling Price (SP) - Cost Price(CP)}$

$\implies Gain = 750 - x$

$\underline{\large{\textbf{Step-3:}}}$
Find the $Gain\%$

We have,
$\bigstar \mathbf{Gain\% = \dfrac{Gain}{CP} \times 100}$

Substituting Values

$\implies 25 = \dfrac{750-x}{x} \times 100$

$\implies \dfrac{25}{100} = \dfrac{750-x}{x}$

$\implies \dfrac{1}{4} = \dfrac{750-x}{x}$

Cross Multiply

$\implies 1 \times x = 4 \times (750-x)$

$\implies x = (4 \times 750)-(4x)$

$\implies x+4x = 3000$

$\implies 5x = 3000$

$\implies x = Rs. 600$ (< Rs. 750)

$\therefore$

$\textsf{The Cost Price of the article, x = \underline{Rs. 600}}$

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