Question

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Answer 1

Let the number of items bought be x.

Total cost of x item is Rs 7500.

(i) Then, price of each items  = Rs 7500/x

Number of items sold after keeping 5 for himself = x-5

Profit per item = Rs 30

Then, total profit =  (Profit per item) × (Total number of items sold) =30(x-5)

With the profit amount he could buy 4 more items than the number of items he bought previously.

Therefore, from the total profit amount, he could buy (4+5)=9 items, because he sold only (x-5) items.

Then, total cost of 9 items = total profit =30(x-5)

(ii) Then, price of each items  = total cost / number of items = 30(x-5)/9 = 10(x-5)/3

Both (i) and (ii) represents the cost of each item, then the two must be equal.

According to problem,

⇒ 7500/x = 10(x-5)/3

⇒ 3*7500 = 10x(x-5)

dividing both sides by 10,

⇒ 3*750 = x(x-5)

⇒ 2250 = x² - 5x

⇒ x² - 5x - 2250 = 0

⇒ x² - 50x + 45x -2250 = 0

⇒ x(x - 50) + 45(x - 50) = 0

⇒ (x + 45)(x - 50) = 0

case 1 :  x + 45 = 0

⇒ x = -45

.

case 2 : x - 50 = 0

⇒ x =  50

So, x = 50 as it cannot be negative...

∴ original cost of each item = 7500/x = 7500/50 = Rs 150

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