Cost price of an article is Rs. A, and a shopkeeper marked that article B%…

2022

Cost price of an article is Rs. A, and a shopkeeper marked that article B% above its cost price. He allows 25% discount on marked price and earned a profit of Rs. (B+20). If the same article is marked up by (B+5)% and allows the same discount and earned a profit of Rs. (B+65), then which of the following is/are correct?

  1. A.

    A/8 = 4B

  2. B.

    29.5B + 20 = A

  3. C.

    None of the above

  4. D.

    1.2A = 36B

  5. E.

    Both 29.5B + 20 = A and 1.2A = 36B

Attempted by 2 students.

Show answer & explanation

Correct answer: E

Concept

When an article costs CP and is marked B% above it, Marked Price = CP×(1 + B/100). A discount d% on the marked price gives Selling Price = MP×(1 − d/100), and Profit = SP − CP. Two profit conditions on the same CP form two equations whose simultaneous solution fixes CP and B; any stated relation is 'correct' only if it holds at that unique solution.

Application

  1. Let CP = A and the first markup = B%. With a 25% discount: SP1 = 0.75·A·(1 + B/100), so Profit1 = 0.75·A·(1 + B/100) − A = B + 20.

  2. With markup (B+5)% and the same 25% discount: SP2 = 0.75·A·(1 + (B+5)/100), so Profit2 = 0.75·A·(1 + (B+5)/100) − A = B + 65.

  3. Subtract the first profit equation from the second: 0.75·A·(5/100) = 45, i.e. 0.0375·A = 45, giving A = 1200.

  4. Substitute A = 1200 into Profit1: 0.75·1200·(1 + B/100) − 1200 = B + 20 → 900 + 9B − 1200 = B + 20 → 8B = 320 → B = 40.

So the unique solution is A = 1200 and B = 40.

Cross-check

Markup 40%: MP = 1200×1.40 = 1680; after 25% discount SP = 1260; profit = 60 = B + 20. ✓ Markup 45%: MP = 1200×1.45 = 1740; after 25% discount SP = 1305; profit = 105 = B + 65. ✓

Evaluating each relation

  • A/8 = 4B: A/8 = 1200/8 = 150, but 4B = 4×40 = 160 — these are unequal, so this relation is false.

  • 29.5B + 20 = A: 29.5×40 + 20 = 1180 + 20 = 1200 = A — this relation holds.

  • 1.2A = 36B: 1.2×1200 = 1440 and 36×40 = 1440 — this relation holds.

Both the relations 29.5B + 20 = A and 1.2A = 36B are satisfied, while A/8 = 4B is not. Hence the combined choice naming those two relations together is the correct one.

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