A tradesman sold an article at a loss of 20%. If the selling price had been increased by ₹100, there would have been a gain of 5%. What was the cost price of the article (₹)?
400
To solve the given problem, we need to determine the cost price of the article based on the given selling conditions. Let's break it down step by step:
Let's denote the cost price of the article as \(C\).
According to the problem, the article was sold at a loss of 20%. This means that the selling price \((SP_1)\) can be expressed as:
\(SP_1 = C - 0.2C = 0.8C\)
If the selling price is increased by ₹100, there would have been a gain of 5%. Therefore, the new selling price \((SP_2)\) can be expressed as:
\(SP_2 = C + 0.05C = 1.05C\)
According to the problem, when the selling price is increased by ₹100, it would result in \(SP_2\). Hence, we can write:
\(SP_2 = SP_1 + 100\)
Substituting the values, we have:
\(1.05C = 0.8C + 100\)
Solving the above equation for \(C\):
\(1.05C - 0.8C = 100\)
\(0.25C = 100\)
\(C = \frac{100}{0.25} = 400\)
Therefore, the cost price of the article is ₹400.
Among the given options, the correct one is: 400.
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