Some amount is equally distributed among some Children. If the no. of children increased by 10, each of them get one rupees less, and if the no. of children reduced by 15 each of them get 3 rupees more. Find the no. of children and total amount given to them:
Answers & Comments
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
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