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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)
    27
  • c)
    18
  • d)
    32
Correct answer is option 'B'. Can you explain this answer?
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A merchant can buy goods at the rate of Rs. 20 per good. The particula...
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
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Most Upvoted Answer
A merchant can buy goods at the rate of Rs. 20 per good. The particula...
, and so on.

Let's represent the number of goods sold as 'n'. Then, the selling price of the nth good can be calculated using the formula:

selling price = 2n

For example, the selling price of the 1st good is 2 x 1 = Rs. 2, the selling price of the 2nd good is 2 x 2 = Rs. 4, and so on.

Now, let's assume that the merchant wants to make a profit of 25% on each good sold. This means that the selling price must be 125% of the cost price.

cost price = Rs. 20
125% of cost price = 1.25 x 20 = Rs. 25

Therefore, the merchant must sell each good for Rs. 25 to make a profit of 25%.

However, the selling price of each good is determined by the formula:

selling price = 2n

So, we need to find the value of 'n' that satisfies the equation:

2n = 25

Taking logarithms on both sides, we get:

n x log(2) = log(25)

n = log(25) / log(2)

n = 4.643

Since 'n' represents the number of goods sold, we can't sell a fractional number of goods. Therefore, the merchant can only sell a maximum of 4 goods in this case.

If the merchant sells 4 goods, the total cost price would be:

cost price = 4 x 20 = Rs. 80

The total selling price would be:

selling price = 2 + 4 + 6 + 8 = Rs. 20

Therefore, the profit made by the merchant would be:

profit = selling price - cost price
profit = 120 - 80
profit = Rs. 40

Hence, the merchant can make a profit of Rs. 40 by selling a maximum of 4 goods at a selling price of Rs. 2n, where n is the number of goods sold.
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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)24b)27c)18d)32Correct answer is option 'B'. Can you explain this answer?
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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)24b)27c)18d)32Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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)24b)27c)18d)32Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)24b)27c)18d)32Correct answer is option 'B'. Can you explain this answer?.
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