Question

Tony sold two pens at the same price, one of which is Reynolds and the other one is Linc. He suffered a loss of 20% on Reynolds whereas a profit of 20% on Linc. In the entire transaction he suffered
1. Loss of 8%
2. Profit of 8%
3. Profit of 4%
4. Loss of 4%

Answer 1

Correct Answer - Option 4 : Loss of 4%

Given:

Selling Price of Reynolds = Selling Price of Linc

Loss on Reynolds = 20%

Profit on Linc = 20%

Formula Used:

Profit % = ((SP - CP)/CP) × 100%

Loss % = ((CP - SP)/CP) × 100%

Calculation:

Let the cost price of Reynolds = Rs. x

Loss on Reynolds = 20%

Loss % = ((CP - SP)/CP) × 100%

⇒ 20 = ((x - SP)/x) × 100

⇒ 1/5 = (x - SP)/x

⇒ x = 5(x - SP)

⇒ x = 5x - 5SP

⇒ 5SP = 4x

⇒ SP = (4/5)x

Selling Price of Reynolds = Rs. (4/5)x

Selling Price of Reynolds = Selling Price of Linc

Selling Price of Linc = Rs. (4/5)x

Profit on Linc = 20%

Profit % = ((SP - CP)/CP) × 100%

⇒ 20 = (((4/5)x - CP)/CP) × 100

⇒ 1/5 =((4/5)x - CP)/CP

⇒ CP = 5((4/5)x - CP)

⇒ CP = 4x - 5CP

⇒ 6CP = 4x

⇒ CP = Rs. (2/3)x

Cost Price of Linc = RS. (2/3)x

Total cost price of Reynolds and Linc = Rs. x + Rs. (2/3)x

⇒ Total cost price of Reynolds and Linc = Rs. (5/3)x

Total selling price of Reynolds and Linc = Rs. (4/5)x + Rs. (4/5)x

⇒ Total selling price of Reynolds and Linc = Rs. (8/5)x

Loss % = ((CP - SP)/CP) × 100%

⇒ Loss % = (((5/3)x - (8/5)x)/(5/3)x) × 100%

⇒ Loss % = 4%

∴ In the entire transaction he suffered a loss of 4%.