Question No 56.A trader buys a consignment of items at the rate of Rs. 150 per item. He sells the first item for Rs.5, second one for Rs.10, third for Rs.15…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?1) 412) 833) 924) 77
Question
Question No 56.A trader buys a consignment of items at the rate of Rs. 150 per item. He sells the first item for Rs.5, second one for Rs.10, third for Rs.15…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?1) 412) 833) 924) 77
Solution
To solve this problem, we first need to understand that the trader is selling each item at an increasing price, with the increase being Rs.5 for each subsequent item. This forms an arithmetic progression series.
The formula for the sum of an arithmetic progression series is n/2 * (a + l) where n is the number of terms, a is the first term, and l is the last term.
We know that the trader wants to make a profit of 40% on the cost price. So, the total selling price should be 140% of the cost price.
Let's assume that the trader sells 'n' items. So, the total cost price for 'n' items would be 150n.
Therefore, 140% of 150n is 210n.
Now, we know that the total selling price is also the sum of the arithmetic progression series. So, we can equate it to the formula of the sum of an arithmetic progression series.
So, 210n = n/2 * (5 + (n-1)*5)
Solving this equation will give us the minimum number of items the trader should sell to make a profit of at least 40%.
Let's solve it:
210n = n/2 * (5 + 5n - 5) 210n = 2.5n^2 84 = n^2 n = sqrt(84)
Since the number of items cannot be in decimals, we round it off to the next whole number. So, the trader should sell at least 10 items to make a profit of at least 40%.
Therefore, none of the options given in the question are correct.
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