Some money is to be distributed equally among children of a locality. If there are 8 children less, every one will get ₹ 10 more and if there are 16 children more, every one will get ₹ 10 less. What is the total amount of money to be distributed ?

Let the total number of children be x and the money given to each child be ₹ y.

So, the total money to be distributed = ₹ xy

If there are 8 children less, each child gets ₹ 10 more.

Total money = (x - 8)(y + 10)

⇒ (x - 8)(y + 10) = xy

⇒ xy + 10x - 8y - 80 = xy

⇒ 10x - 8y = 80 ……………….(1)

If there are 16 children more, each child gets ₹ 10 less.

Total money = (x + 16)(y - 10)

⇒ (x + 16)(y - 10) = xy

⇒ xy - 10x + 16y - 160 = xy

⇒ 10x - 16y = -160 ……………….(2)

Subtracting equation (2) from equation (1), we get:

$\begin{matrix} & 10x & - & 8y & = & 80 \ & 10x & - & 16y & = & -160 \ & - & &+ & & + \ \hline & & & 8y & = & 240 \ \Rightarrow & & & y & = & \dfrac{240}{8} \ \end{matrix}$

⇒ y = 30

Substituting y = 30 in equation (1), we get:

⇒ 10x - 8 $\times$ 30 = 80

⇒ 10x - 240 = 80

⇒ 10x = 80 + 240

⇒ 10x = 320

⇒ x = $\dfrac{320}{10}$

⇒ x = 32

Total money = xy = 32 x 30 = 960

Hence, the total money to be distributed is ₹ 960.