An article passing through two hands is sold at a total profit of 40% of the original cost price. If the first dealer makes a profit of 30%, then the profit percentage made by the second dealer is:
- (a)
- (b)
- (c)
- (d)
Answer
Why
Correct — B. Put the original cost price at ₹100, because every percentage in the stem is measured against it.
First dealer sells at 100 + 30% of 100 = ₹130, and that ₹130 is the second dealer's cost.
The chain's total profit is 40% of the ORIGINAL cost, so the final selling price = ₹140.
Second dealer's profit = 140 − 130 = ₹10, earned on a cost of ₹130.
10⁄130 = 1⁄13 of his cost = 100⁄13 % = 7 9⁄13 % → option (b), which prints 7 9⁄13 %.
Why the others are wrong
- (a)Option (a) is 7 1⁄13 % = 92⁄13 %. On a cost of ₹130 that is ₹9.20 of profit, ending the chain at ₹139.20 — an overall profit of 39.2%, not the 40% the stem fixes.
- (c)Option (c) is 6 3⁄13 % = 81⁄13 %, or ₹8.10 on ₹130. The article would finish at ₹138.10, leaving the two dealers with 38.1% between them.
- (d)Option (d) is 8 6⁄13 % = 110⁄13 %, which is ₹11 on ₹130. The final price becomes ₹141, so the chain would have made 41% — one point too much.
Concept
A percentage means nothing until you know what it is a percentage of, and this stem runs two different bases.
The first dealer's 30% is on the original cost. The overall 40% is on the original cost too — the stem says so. But the second dealer's profit is on his own cost, which is the first dealer's selling price, not the original ₹100.
So the money moves 100 → 130 → 140, and only the last leg is measured on 130. Multiplying factors rather than adding percentages keeps the bases straight: 1.30 × (1 + x) = 1.40.
The phrase total profit of 40% of the original cost price is doing the real work here. It fixes the final selling price at ₹140 on a ₹100 base.
Read that base wrongly — as 40% of what the second dealer paid — and every line after it is wrong even though the arithmetic is clean.
Key facts
- Profit percentage is always measured on the cost price of the person making it, never on the original cost further back in the chain.
- Successive gains multiply: a 30% profit followed by an x% profit leaves 1.30 × (1 + x) times the original cost.
- For two successive profits of a% and b%, the overall profit is a + b + ab⁄100 per cent.
- 1⁄13 written as a percentage is 100⁄13 %, that is 7 9⁄13 % or about 7.69%.
Study next
Common traps
- Subtracting the rates, 40 − 30 = 10, and reporting 10% as the second dealer's profit
- Measuring the second dealer's ₹10 gain on the original ₹100 rather than on the ₹130 he paid
- Stopping at the fraction 1⁄13 and forgetting to multiply by 100 to make it a percentage
SSC writes this as a chain sale and states which base the final percentage sits on — read that clause before you start computing.
The same moving-base idea, dressed as a mark-up followed by two discounts, runs at 26 Sep 2024, 16:00, Quant Q.21, where the answer is a gain of 8% on cost and not on the marked price.
Related PYQs
No directly related past PYQ was found.