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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