Question

An article is bought for ₹ x and is sold at the profit of x%. If its selling price is ₹ 56, the cost price is ______.

Options

• ₹ 60

• ₹ 50

• ₹ 40

• ₹ 28

Answer 1

An article is bought for ₹ x and is sold at the profit of x%. If its selling price is ₹ 56, the cost price is ₹ 40.

Explanation:

Given the cost price of an article = ₹ x

S.P of an article = ₹ 56

∴ Profit = S.P – C.P = (56 – x)

Since profit % = `"Profit"/"C.P" xx 100%`

`\implies x = (56 - x)/x xx 100`

`\implies` x² = 5600 – 100x

`\implies` x² + 100x – 5600 = 0

`\implies` x² – 40x + 140x – 5600 = 0

`\implies` x(x – 40) + 140(x – 40) = 0

`\implies` (x – 40)(x + 140) = 0

Either x – 40 = 0 or x + 140 = 0

`\implies` x = 40 or x = – 140

`\implies` x = 40   ...[∵ x > 0]