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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)9
- b)16
- c)27
- d)36
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 particula...
, and so on. If the merchant sells the goods in this pattern, how much total money will he make after selling 10 goods?
The merchant sells the goods at a rate of Rs. 2 more than the previous one. So, the selling price of the n-th good will be 2n.
To find the total money made after selling 10 goods, we need to find the sum of the selling prices from the first to the tenth good.
The sum of the first n terms of an arithmetic sequence can be found using the formula:
Sum = (n/2)(first term + last term)
In this case, the first term is 2 and the last term is 2n. So, the sum of the first n goods sold will be:
Sum = (n/2)(2 + 2n)
For n = 10, the sum will be:
Sum = (10/2)(2 + 2*10)
= 5(2 + 20)
= 5(22)
= 110
Therefore, the merchant will make a total of Rs. 110 after selling 10 goods.
The merchant sells the goods at a rate of Rs. 2 more than the previous one. So, the selling price of the n-th good will be 2n.
To find the total money made after selling 10 goods, we need to find the sum of the selling prices from the first to the tenth good.
The sum of the first n terms of an arithmetic sequence can be found using the formula:
Sum = (n/2)(first term + last term)
In this case, the first term is 2 and the last term is 2n. So, the sum of the first n goods sold will be:
Sum = (n/2)(2 + 2n)
For n = 10, the sum will be:
Sum = (10/2)(2 + 2*10)
= 5(2 + 20)
= 5(22)
= 110
Therefore, the merchant will make a total of Rs. 110 after selling 10 goods.
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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
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
The question is " If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?"
He should sell a minimum of 27 goods.
He should sell a minimum of 27 goods.
Hence, the answer is 27.
Choice C is the correct 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)9b)16c)27d)36Correct answer is option 'C'. Can you explain this answer?
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