Question : A man sells an article at a gain of 15%. If he had bought it at 10% less and sold it for Rs. 4 less, he would have gained 25%. The cost price of the article is:
Option 1: Rs. 140
Option 2: Rs. 150
Option 3: Rs. 160
Option 4: Rs. 185
Correct Answer: Rs. 160
Solution :
Here CP denotes cost price and SP denotes selling price.
Let CP = Rs. $x$
SP = $x(\frac{100+Profit\%}{100})$
⇒ SP = $x(\frac{100+15}{100})$
⇒ SP = $x(\frac{115}{100})$
New CP = $x-\frac{10}{100}x$
⇒ New CP = $\frac{90}{100}x$
New SP = $\frac{115}{100}x-4$
Profit = $25$%
New Profit = $\frac{115}{100}x-4 - \frac{90}{100}x$
⇒ New Profit = $\frac{25}{100}x-4$
Given:
$\frac{\frac{25}{100}x-4}{\frac{90}{100}x} \times 100 = 25$
⇒ $\frac{25}{100}x-4 = 0.25(\frac{90}{100})x$
⇒ $0.25x-4 = 0.25 \times 0.9x$
⇒ $0.25x-0.225x = 4$
⇒ $0.025x=4$
⇒ $x= 160$
Hence, the correct answer is Rs. 160.
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