Question

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?

1. Rs. 20
2. Rs. 18
3. Rs. 15
4. Rs. 22

Answer 1

Correct Answer - Option 1 : 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