Question

Traders A and B buy two goods for Rs. 1000 and Rs. 2000 respectively. Trader A marks his goods up by x%, while trader B marks his goods up by 2x% and offers a discount of x%. If both make the same profit, find x.

1. 25%
2. 12.5%
3. 37.5%
4. 40%

Explanatory Answer

SP of trader A = 1000 (1 + x)
Profit of trader A = 1000 (1 + x) - 1000

MP of trader B = 2000 (1 + 2x)
SP of trader B = 2000 (1 + 2x) (1 - x)
Profit of trader B = 2000 (1 + 2x) (1 - x)- 2000

Both make the same profit => 1000 (1 + x) – 1000 = 2000(1 + 2x) (1 - x) - 2000

1000x = 2000 – 4000x² + 4000x – 2000x - 2000
4000x² -1000x = 0
1000x (4x - 1) = 0
x = 25%

Answer Choice (A)