Answer:
[tex]\[\frac{1}{24}\][/tex]
Step-by-step 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 = [tex]\[\frac{7x}{8}\][/tex]
Remaining batteries = [tex]\[x-\frac{7x}{8}\][/tex]
= [tex]\[\frac{x}{8}\][/tex]
Two third of the remaining batteries are sent to charity.
So the total number of batteries sent to charity= [tex]\[\frac{2}{3} * \frac{x}{8}\][/tex]
= [tex]\[\frac{x}{12}\][/tex]
Remaining batteries are faulty.
So the total number of faulty batteries = [tex]\[\frac{x}{8} - \frac{x}{12}\][/tex]
= [tex]\[\frac{3x - 2x}{24}\][/tex]
= [tex]\[\frac{x}{24}\][/tex]
So the faction of batteries which are faulty =
= [tex]\[\frac{x}{24} \div x\][/tex]
= [tex]\[\frac{1}{24}\][/tex]