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A businessman bought some items for 7500. He kept 5 items for himself and sold the remaining items at a profit of 30 per item. From the amount received in this deal, he could buy 4 more items. Find the original price of each item.

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150

60

230

140

answer is A.

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Detailed Solution

Concept- In order to solve the given question we will use the basic arithmetic of comparing quantities to find the answer of the question.

(x - 5) (y + 30) - 7509 = 4 \times y

(x - 5) [(\frac{7500}{x}) + 30] - 7500 = 4 y

(x - 5) [(\frac{7500 + 30 x}{x}] - 7500 = 4 y

(x - 5) (7500 + 30 x) - 7500 x = 4 xy

7500 x + 30 x^{2} - 37500 - 150 x - 7500 x = 4 xy

30 x^{2} + 7500 x - 150 x - 7500 x - 37500 = 4 \times 7500

30 x^{2} - 150 x - 37500 - 30000 = 0

30 x^{2} - 150 x - 67500 = 0

30 (x^{2} - 5 x - 2250) = 0

x^{2} - 5 x - 2250 = 0

Then,

x = - 45, + 50

As we know, cost cannot be negative .

then, x = 50

Therefore ,

Price per item = \frac{7500}{50} = 150

Hence, the correct answer is option 1.

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