Traders A and B buy two goods for Rs. 1000 and Rs. 2000 respectively. Trader A…
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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%
Attempted by 14 students.
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Correct answer: A
Let r = x/100 (so r is x expressed as a decimal).
Trader A: Cost price = 1000. Markup x% ⇒ selling price = 1000(1 + r). Profit = 1000(1 + r) − 1000 = 1000r.
Trader B: Cost price = 2000. Markup 2x% ⇒ marked price = 2000(1 + 2r). After discount x% ⇒ selling price = 2000(1 + 2r)(1 − r).
Profit = 2000[(1 + 2r)(1 − r) − 1] = 2000(r − 2r^2).
Equate the two profits:
1000r = 2000(r − 2r^2)
Simplify: 1000r = 2000r − 4000r^2 ⇒ 0 = 1000r − 4000r^2 = 1000r(1 − 4r).
Since the profit is non-zero, r ≠ 0, so 1 − 4r = 0 ⇒ r = 1/4.
Therefore x = 100 × r = 100 × 1/4 = 25%.
Answer: 25%.