Question

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

Answer 1

Answer:

80........................

Answer 2

9th

Maths

Linear Equations in Two Variable

Linear Equations

Some money is to be distrib...

MATHS

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?

MEDIUM

ANSWER

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. 10more.

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. 10less.

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=8240=30

From equation (1),

10x=80+8y

10x=320

x=10320=32

Total money  =xy=32×30

=Rs.960