Question

Steve bought two cameras for Rs. 41000. He sold one at a loss of 15% and the other at a profit of 20%. If the selling price of each camera is the same, then their cost prices are respectively
1. Rs. 15000 and Rs. 26000
2. Rs. 20000 and Rs. 21000
3. Rs. 24000 and Rs. 17000
4. Rs. 30000 and Rs. 11000

Answer 1

Correct Answer - Option 3 : Rs. 24000 and Rs. 17000

Given:

Cost price of both cameras = Rs. 41000

Loss on first camera = 15%

Profit on second camera = 20%

Formula Used:

Loss % = ((CP - SP)/CP) × 100%

Profit % = ((SP - CP)/CP) × 100%

Calculation:

Let the cost price of first camera = Rs. x

and the cost price of second camera = Rs. y

Let selling price of each camera = Rs. z

Loss on first camera = 15%

Loss % = ((CP - SP)/CP) × 100%

⇒ 15 = ((x - z)/x) × 100

⇒ 3/20 = (x - z)/x

⇒ 3x = 20(x - z)

⇒ 3x = 20x - 20z

⇒ 17x = 20z

⇒ x = (20/17)z

Profit on second camera = 20%

Profit % = ((SP - CP)/CP) × 100%

⇒ 20 = ((z - y)/y) × 100

⇒ 1/5 = (z - y)/y

⇒ y = 5(z - y)

⇒ y = 5z - 5y

⇒ 6y = 5z

⇒ y = (5/6)z

∵ x + y = 41000

⇒ (20/17)z + (5/6)z = 41000

⇒ (205/102)z = 41000

⇒ z = 20400

Selling Price of each camera = Rs. 20400

 x = (20/17)z

⇒ x = (20/17) × 20400

⇒ x = 24000

 y = (5/6)z

⇒ y = (5/6) × 20400

⇒ y = 17000

∴ Cost Price of cameras are Rs. 24000 and Rs. 17000 respectively.