Mathematics

A man buys an article for ₹ x and sells it for ₹ 56 at a gain of x%. Find the value of x.

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Given,

Cost price of given article = ₹ x

Gain % after selling article = x%

Selling price = ₹ 56

By formula,

⇒ Selling price = $\dfrac{(100 + x)}{100}$ × cost price

⇒ 56 = $\dfrac{(100 + x)}{100}$ × x

⇒ 56 × 100 = x(100 + x)

⇒ 5600 = 100x + x²

⇒ x² + 100x - 5600 = 0

⇒ x² + 140x - 40x - 5600 = 0

⇒ x(x + 140) - 40(x + 140) = 0

⇒ (x - 40)(x + 140) = 0

⇒ (x - 40) = 0 or (x + 140) = 0 [Using zero-product rule]

⇒ x = 40 or x = -140

Since, cost price and gain% cannot be negative.

Thus, x = 40.

Hence, value of x = 40.

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