Question

A factory produces some batteries daily. 7/8 of the batteries are packaged immediately. 2/3 of the

remaining batteries are sent to charity and the rest are faulty.
(a) Find the fraction of batteries that are faulty in the batch.​

Answer 1

`\[(1)/(24)\]`

Explanation:

Let the total number of batteries produced daily be represented by x.

7/8 of the batteries are packaged immediately.

So the total number of packaged batteries =
`\[(7x)/(8)\]`

Remaining batteries =
`\[x-(7x)/(8)\]`

=
`\[(x)/(8)\]`

Two third of the remaining batteries are sent to charity.

So the total number of batteries sent to charity=
`\[(2)/(3) * (x)/(8)\]`

=
`\[(x)/(12)\]`

Remaining batteries are faulty.

So the total number of faulty batteries =
`\[(x)/(8) - (x)/(12)\]`

=
`\[(3x - 2x)/(24)\]`

=
`\[(x)/(24)\]`

So the faction of batteries which are faulty =

=
`\[(x)/(24) / x\]`

=
`\[(1)/(24)\]`