Question

A man bought certain number of glass vessels for₹600. 2 of them broke then he sold the remaining for ₹10 more than he has given for it thereby gaining ₹50 on the whole, How many of glass vessel did he buy and also.find the cost of each glass be X

Answer 1

$\huge\underline\mathfrak\red{Answer}$

Let x be the number that he bought, and y be what he paid for each.

x * y = 600

(x-2) * (y+10) = 600 + 50

xy = 600

y = 600 / x

xy + 10x - 2y - 20 = 650

600 + 10x - 2y - 20 = 650

10x - 2y = 70

5x - y = 35

5x - (600/x) = 35

5x^2 - 600 = 35x

5x^2 - 35x - 600 = 0

x^2 - 7x - 120 = 0

(x + 8)(x - 15) = 0

x = -8 or x = 15

Because he obviously bought a positive quantity, we can disregard the negative root. He bought 15 of them.

To check:

600 / 15 = 40, so he paid Rs.40 for each.

He broke 2, and sold the remaining 13 at Rs.50 each, for a total of Rs.650.

Therefore, he gained Rs.50 overall.