Question

Grabdfather distributed some amount among his grand children.If there were 3 grand childrens less every one would hav got rupess 60 more.however if he had 2 more grandchildren,each one would have got rupees 20 less.Give number of grand children and amount received by them.

Answer 1

let no: of grandchildren be x and amount of money distributed to each grandchild be y
∴ total amount = xy
now if there were 3 grandchildren less everyone would get 60 rupees more
now, no:of grandchildren = (x - 3)
amount distributed to each grandchild = (y + 60)
as total amount still remains the same
∴(x - 3) * (y + 60) = xy
⇒xy -3y +60x - 180 = xy
60x - 3y = 180 ..............(i)

also when two more grandchildren are there each one gets 20 rupees less
now , no: of grandchildren = (x + 2)
amount distributed among them = (y - 20)
as amount remains the same
∴(x + 2) * (y - 20) = xy
⇒xy +2y - 20x - 40 = xy
2y - 20x = 40 
when whlole thing is multiplied by 3
6y - 60x = 120 ......(ii)
adding (i) and (ii)
6y -60x +60x - 3y = 180 + 120
3y = 300
 y = 100
putting y = 100 in (ii)
600 - 60x = 120
10 - x = 2
x = 8
therefore there are 8 grandchildren and they received 100 rupees each