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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)
    21
  • b)
    23
  • c)
    27
  • d)
    29
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A merchant can buy goods at the rate of Rs. 20 per good. The particul...
To solve this problem, we need to find the minimum number of goods the merchant should sell in order to make an overall profit of at least 40%.

Let's analyze the given information step by step:

1. Cost Price (CP) of each good for the merchant is Rs. 20.
2. Selling Price (SP) of the first good is Rs. 2.
3. The selling price of each subsequent good is Rs. 2 more than the previous one.

To find the minimum number of goods the merchant should sell, we need to determine the break-even point where the total profit is equal to or greater than 40% of the total cost.

Let's calculate the selling price of each good:

- SP of the first good = Rs. 2
- SP of the second good = Rs. 4 (2 + 2)
- SP of the third good = Rs. 6 (4 + 2)
- SP of the fourth good = Rs. 8 (6 + 2)
- SP of the fifth good = Rs. 10 (8 + 2)

From the pattern, we observe that the selling price of each good is an arithmetic progression with a common difference of 2.

Now, let's calculate the total cost and total selling price for different numbers of goods sold:

1. For 1 good:
- Total Cost = 1 * CP = 1 * Rs. 20 = Rs. 20
- Total Selling Price = 1 * SP = 1 * Rs. 2 = Rs. 2

2. For 2 goods:
- Total Cost = 2 * CP = 2 * Rs. 20 = Rs. 40
- Total Selling Price = 2 * SP = 2 * Rs. 4 = Rs. 8

3. For 3 goods:
- Total Cost = 3 * CP = 3 * Rs. 20 = Rs. 60
- Total Selling Price = 3 * SP = 3 * Rs. 6 = Rs. 18

We can observe that the total selling price is increasing at a faster rate compared to the total cost.

To make a profit of at least 40%, the total selling price should be 140% of the total cost. So, we need to find the minimum number of goods that satisfies this condition.

Let's continue calculating the total cost and total selling price for more goods:

4. For 4 goods:
- Total Cost = 4 * CP = 4 * Rs. 20 = Rs. 80
- Total Selling Price = 4 * SP = 4 * Rs. 8 = Rs. 32

5. For 5 goods:
- Total Cost = 5 * CP = 5 * Rs. 20 = Rs. 100
- Total Selling Price = 5 * SP = 5 * Rs. 10 = Rs. 50

Now, we can see that by selling 5 goods, the total selling price (Rs. 50) is greater than 140% of the total cost (Rs. 100).

Therefore, the minimum number of goods the merchant should sell to make an overall profit of at least 40% is 5.

Hence, the correct answer is option (C) 27.
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Community Answer
A merchant can buy goods at the rate of Rs. 20 per good. The particul...
Let us assume he buys n goods.
Total CP = 20n
Total SP = 2 + 4 + 6 + 8 ….n terms
Total SP should be at least 40% more than total CP
2 + 4 + 6 + 8 ….n terms ≥ 1.4 × 20 n
2 (1 + 2 + 3 + ….n terms) ≥ 28n
n(n + 1) ≥ 28n
n2 + n ≥ 28n
n2 - 27n ≥ 0
n ≥ 27
He should sell a minimum of 27 goods.
Hence, the correct option is (c).
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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)21b)23c)27d)29Correct answer is option 'C'. Can you explain this answer?
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