Question : The reduction of Rs. 12 in the selling price of an article will change a 5% gain into $2\frac{1}{2}$% loss. The cost price of the article is:
Option 1: Rs. 140
Option 2: Rs. 160
Option 3: Rs. 80
Option 4: Rs. 100
Correct Answer: Rs. 160
Solution :
Let the cost price be $x$
Gain = 5%
Selling Price = $\frac{105x}{100}$
New selling price = $\frac{105x}{100} - 12$
Now there is a loss of 2.5%
So, $x \times \frac{100-2.5}{100} = \frac{105x}{100} - 12$
⇒ $\frac{97.5x}{100} = \frac{105x}{100} - 12$
⇒ $97.5x = 105x - 1200$
⇒ $7.5x = 1200$
⇒ $x =160$
Hence, the correct answer is Rs. 160.
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