Answer:
![\[(1)/(24)\]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/e9pl1cueuveluimucsiatvat2v9s0edy0m.png)
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 =
![\[(7x)/(8)\]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/zywjs31ncpf9a40gc7lgtbckjo3t98gtpo.png)
Remaining batteries =
![\[x-(7x)/(8)\]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/gro89co5dvg5a0b7ookm2ci8fhl86g01gv.png)
=
![\[(x)/(8)\]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/gdnprjh6f4kjkrmiztzjwxo2zdv5y3vijo.png)
Two third of the remaining batteries are sent to charity.
So the total number of batteries sent to charity=
![\[(2)/(3) * (x)/(8)\]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/c29y74e0jmy80p2kyupsuax0lcrtrzxub2.png)
=
![\[(x)/(12)\]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/xqiuqw4q7mhn76ng82jbyelki1cc58dt5i.png)
Remaining batteries are faulty.
So the total number of faulty batteries =
![\[(x)/(8) - (x)/(12)\]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/7uodi4lwchfekzx93bohm0o02a3la260jm.png)
=
![\[(3x - 2x)/(24)\]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/j6fvev120q7kobarl0qtn1b0chprpdk1qs.png)
=
![\[(x)/(24)\]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/w7j4uuq4sokis0djgjfgudxx6grgwzivd3.png)
So the faction of batteries which are faulty =
=
![\[(x)/(24) / x\]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/qzb6d5odwcrnj9orxqfheh15jgrr04okgs.png)
=
![\[(1)/(24)\]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/e9pl1cueuveluimucsiatvat2v9s0edy0m.png)