Question

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31. 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 ?​

Answer 1

Step-by-step explanation:

Let the total number of children =x

Let the money given to each student =Rs.y

So, the total money =x×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)×(y+10)

⇒(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)×(y−10)

⇒(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=

8

240

=30

From equation (1),

10x=80+8y

10x=80+240

10x=320

x=

10

320

=32

Total money =xy=32×30

=Rs.960