Question : A man bought an article and sold it at a gain of 10%. If he had bought the article at 20% less and sold it for INR 1,000 more, he would have made a profit of 40%. The cost price of the article (in INR) is:
Option 1: 50,000
Option 2: 60,000
Option 3: 40,000
Option 4: 25,000
Correct Answer: 50,000
Solution :
Here cost price is denoted by CP, selling price is denoted by SP.
Let the original CP of the article be $x$.
Case 1:
SP = $\frac{{100 + \text{Profit%}}}{{100}} \times$ CP
⇒ SP = $\frac{{100 + 10\%}}{{100}} \times x$
⇒ SP = $\frac{{11x}}{{10}}$
Case2:
The new CP is 20% less than the original CP and sold for INR 1000 more
New CP = $x$ – 20% of $x$
⇒ New CP = $x - \frac{20}{100} \times x$
⇒ New CP = $\frac{80}{100} \times x$
⇒ New CP = $\frac{4}{5} \times x$
According to the question,
(SP + 1000) – New CP = 40% of New CP
⇒ $\left(\frac{11x}{10} + 1000\right) - \frac{4x}{5} = \frac{40}{100} \times \frac{4x}{5}$
⇒ $\frac{11x}{10} - \frac{4x}{5} + 1000 = \frac{8x}{25}$
⇒ $\frac{11x - 8x}{10} - \frac{8x}{25} = -1000$
⇒ $\frac{3x}{10} - \frac{8x}{25} = -1000$
⇒ $\frac{15x - 16x}{50} = -1000$
⇒ $-\frac{x}{50} = -1000$
$\therefore x$ = INR 50,000
So,
the cost price of the article is INR 50,000.
Hence, the correct answer is 50,000.
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