Question

Grandfather distributed some amount among his grand children.If there were 3 grandchildren less every one would have got rupees 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

Answer:

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Step-by-step explanation:

Let the total number of grandchildren = x

Let the amount received by each grandchild = Rs y

Total money distributed by grandfather = Rs xy

CASE 1:Number of grandchildren = x-3

amount received by each grandchild = Rsy+60

Total money distributed by grandfather = Rs xy

⇒x-3y+60 = xy

⇒xy + 60x - 3y - 180 = xy

⇒60x - 3y = 180

⇒20x - y = 60 .......

1CASE 2:Number of grandchildren = x+2

amount received by each grandchild = Rsy-20

Total money distributed by grandfather = Rs xy

⇒x+2y-20 = xy

⇒xy -20x + 2y - 40 = xy

⇒-20x + 2y = 40

⇒-10x + y = 20

..........2Adding 1 and 2, we get 10x = 80

⇒x = 8

Put x = 8 in 1,

we get 20 × 8 - y = 60

⇒160 - y = 60

⇒y = 100

So, total number of grandchildren = 8

amount received by each grandchild = Rs 100