Question

40 Marbles are equally divided among A certain number of children if there were 2 children less each would have received 1 more marble find the number of children​

Answer 1

Step-by-step explanation:

Let,

Number of children be "n"

Number of marbles each child got be "x"

Then in first case

40/n = x ....(1)

In second case

40/(n - 2) = x + 1

From equation (1)

40/(n - 2) = 40/n + 1

40/(n - 2) - 40/n = 1

40[1/(n - 2) - 1/n] = 1

1/(n - 2) - 1/n = 1/40

n/[n(n - 2)] - (n - 2)/[n(n - 2)] = 1/40

[n - (n - 2)]/[n(n - 2)] = 1/40

2/(n² - 2n) = 1/40

n² - 2n = 80

n² - 2n - 80 = 0

(n - 10)(n + 8) = 0

n = 10 or n = -8

"n" can't be negative.

Hence, number of children are 10.