Question

Williiam lost 25% of his marble,gave 1/6 of the remainder to his.Brother and had 120 marbles left.How many marbles did he have at first?

Answer 1

Number of marbles with Williams at the starting = 192

Explanation:

Let total number of marbles with Williams = m

He lost marbles = 25% of the total number

=
`(25)/(100)* m`

=
`(m)/(4)`

Remaining marbles with Williams = m -
`(m)/(4)`

=
`(3m)/(4)`

He gave marbles to his brother =
`(1)/(6)`th of the remaining marbles

=
`(1)/(6)* (3m)/(4)`

=
`(m)/(8)`

Remaining marbles after giving marbles to his brother = 120

Therefore,
`(3m)/(4)-(m)/(8)=120`

`(6m)/(8)-(m)/(8)=120`

`(5m)/(8)=120`

m =
`(120* 8)/(5)`

m = 192

Number of marbles with Williams at the starting = 192