Question

Stephen & Richard share a lottery win of £2950 in the ratio 2 : 3. Stephen then shares his part between himself, his wife & their son in the ratio 3 : 5 : 2. How much more does his wife get over their son?

Answer 1

Stephen's wife got £354 more than his son.

Explanation:

Given:

Amount of Lottery = £2950

Now Given:

Stephen & Richard share a lottery amount in the ratio 2 : 3

Let the common factor between them be 'x'.

So we can say that;

`2x+3x=2950\\\\5x = 2950`

Dividing both side by 5 we get;

`(5x)/(5)=(2950)/(5)\\\\x = 590`

So we can say that;

Stephen share would be =
`2x =2* 590 = \£1180`

Now Given:

Stephen then shares his part between himself, his wife & their son in the ratio 3 : 5 : 2.

Let the common factor between them be 'y'.

So we can say that;

`3y+5y+2y=1180\\\\10y=1180`

Dividing both side by 10 we get;

`(10y)/(10)=(1180)/(10)\\\\y=118`

So Stephen's wife share =
`5y = 5* 118= \£590`

And Stephen's son share =
`2y=2*118 =\£236`

Now we need to find how much more her wife got then her son.

To find how much more her wife got than her son we will subtract Stephen's son share from Stephen's wife share.

framing in equation form we get;

Amount more her wife got than her son =
`590-236 = \£354`

Hence Stephen's wife got £354 more than his son.