online cat preparation time CAT Preparation - Linear Equations Questions 04

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 non-zero profit, find x.

(a) 25%




(b) 12.5%
(c) 37.5%




(d) 40%

DETAILED SOLUTION

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)

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online cat preparation time CAT Preparation - Linear Equations Questions 04
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