Question : An article is sold at a 25% loss. If its cost price is doubled and the selling price is increased by INR 660, then there is a profit of 20%. What is the original cost price of the article?
Option 1: INR 480
Option 2: INR 500
Option 3: INR 400
Option 4: INR 360
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Correct Answer: INR 400
Solution : Given: An article is sold at a 25% loss. If its cost price is doubled and the selling price is increased by INR 660, then there is a profit of 20%. Profit = SP – CP Loss = CP – SP Loss percentage = $\frac{\text{Loss}}{CP}\times 100$ Profit percentage = $\frac{\text{Profit}}{CP}\times 100$ Where SP is the selling price and CP is the cost price. According to the question, $\frac{CP–SP}{CP}\times 100=25$ -------------(1) ⇒ $1–\frac{SP}{CP}=0.25$ ⇒ $\frac{SP}{CP}=0.75$ ⇒ $SP=0.75CP$ Also, $\frac{SP+660–2CP}{2CP}\times 100=20$ -------------(2) Substitute the value of SP in the equation (2), ⇒ $\frac{0.75CP+660–2CP}{2CP}\times 100=20$ ⇒ $\frac{660–1.25CP}{2CP}=0.2$ ⇒ $660–1.25CP=0.4CP$ ⇒ $1.65CP=660$ ⇒ $CP=\frac{660}{1.65}=$ INR 400 Hence, the correct answer is INR 400.
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