A merchant can buy goods at the rate of Rs. 20 per good. The particular good…
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A merchant can buy goods at the rate of Rs. 20 per good. The particular good is part of an overall collection and the value is linked to the number of items that are already on the market. So, the merchant sells the first good for Rs. 2, second one for Rs. 4, third for Rs. 6…and so on. If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?
- A.
24
- B.
18
- C.
27
- D.
32
Attempted by 39 students.
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Correct answer: C
Let n be the number of goods sold.
Total cost price (CP) = 20n.
Total selling price (SP) = 2 + 4 + 6 + ... + 2n = 2(1 + 2 + ... + n) = n(n + 1).
Require an overall profit of at least 40%, so SP ≥ 1.4 × CP = 28n.
Thus n(n + 1) ≥ 28n. For n > 0 divide both sides by n to get n + 1 ≥ 28, so n ≥ 27.
Minimum integer value is n = 27.
Check: for n = 27, SP = 27 × 28 = 756 and CP = 20 × 27 = 540. Profit = 756 − 540 = 216, which is 40% of 540, so the condition is satisfied exactly.
Therefore the minimum number of goods he should sell is 27.