Question

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

Answer 1

Let the total number of children $=x$

Let the money given to each student $=Rs.y$

So, the total money $=x\times y$

If there are $8$ children less, everyone will get Rs. $10$ more.

So, everyone will get Rs. $10+y$

Total amount of money $=(x-8)\times (y+10)$

$\Rightarrow (x-8)(y+10)=xy$

$xy+10x-8y-80=xy$

$10x-8y-80=0$

$10x-8y=80$ ....................... (1)

If there are $16$ children more, everyone will get Rs. $10$ less.

So, everyone will get Rs. $y-10$

Total amount of money $=(x+16)\times (y-10)$

$\Rightarrow (x+16)(y-10)=xy$

$xy-10x+16y-160=xy$

$-10x+16y-160=0$

$-10x+16y=160$ ..................... (2)

By adding (1) and (2),

$-8y+16y=80+160$

$8y=240$

$y=\frac{240}{8}=30$

From equation (1),

$10x=80+8y$

$10x=80+240$

$10x=320$

$x=\frac{320}{10}=32$

Total money $=xy=32\times 30$

$=Rs.960$