Question : A trader sold an article at a gain of 20%. Had he purchased it for 40% more and sold it for Rs. 24 less, he would have incurred a loss of 20%. What is the cost price (in Rs.) of the article?
Option 1: Rs. 150
Option 2: Rs. 300
Option 3: Rs. 450
Option 4: Rs. 600
Correct Answer: Rs. 300
Solution :
Here, SP is the selling price and CP is the cost price.
Let the CP of the article be $x$.
Give, Profit = 20%
⇒ SP = $1.2x$
New CP = $x$ + 40% of $x$ = $\small1.4x$
New SP = $\small1.2x - 24$
$\therefore$ Loss = $\small1.4x - (1.2x - 24) = 0.2x + 24$
According to the question,
$\frac{(0.2x + 24)\times100}{1.4x} = 20\%$
⇒ $\frac{0.2x+24}{1.4x}=\frac{20}{100}$
⇒ $\frac{0.2x+24}{1.4x}=\frac{1}{5}$
⇒ $x + 120 = 1.4x$
⇒ $0.4x =$ 120
$\therefore x=$ Rs. 300
Hence, the correct answer is Rs. 300.
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