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Question
A dealer sells a toy for ₹ 24 and gains as much percent as the cost price of the toy. Find the cost price of the toy.
Solution
Selling price (S.P.) of the toy = ₹ 24
Let the cost price (C.P.) of the toy be ₹ x.
∴ Gain% = x%
Gain% = `("S.P." - "C.P.")/"C.P." xx 100`
∴ x = `(24 - "x")/"x" xx 100`
∴ x2 = (24 – x)100
∴ x2 = 2400 – 100x
∴ x2 + 100x – 2400 = 0
∴ x2 + 120x – 20x – 2400 = 0
∴ x(x + 120) – 20(x + 120) = 0
∴ (x + 120) (x – 20) = 0
∴ x + 120 = 0 or x – 20 = 0
∴ x = – 120 or x = 20
But, the cost price cannot be negative.
∴ x = 20
∴ The cost price of the toy is ₹ 20.
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