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A boy sold his cap for Rs. 24 and got a profit percentage numerically equal to the cost price. What will be the cost price of the cap?

A boy sold his cap for Rs. 24 and got a profit percentage numerically equal to the cost price. What will be the cost price of the cap? Correct Answer Rs. 20

Given 

The selling price of cap = Rs 24 

Formula Used 

Cost price = {Selling Price/(100 + profit%)} × 100 

Calculation 

Let the cost price be x 

⇒ x = 24/(100 + x) × 100 

⇒ x2 + 100x - 2400 = 0 

⇒ x2 + 120x - 20x - 2400 = 0

⇒ x(x + 120) - 20(x + 120) =

⇒ (x - 20)( x + 120)

We get x = 20 and x = - 120

(As cost price cannot be negitive)

So, cost price = Rs 20 

∴ The cost price is Rs 20

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