Question

A cistern can be filled by one tap in 8 hours and by another in 4 hours . How long will it take to fill the cistern .If both taps are opened together ?​

Answer 1

Given :

• time taken by one tap to fill the cistern = 6 hours
• time taken by another tap to fill the cistern = 4 hours

To Find :

• How long will it take to fill the cistern when both tapa are opened together.

Solution :

Total part of the cistern = 1

so, one tap filled in 1 hour = 1/4

and another tap filled in 1 hour = 1/6

then, both tap together filled the cistern in 1 hour,

$: \implies \frac{1}{4} + \frac{1}{6} \\ \\ : \implies \frac{3 + 2}{12} \\ \\ : \implies \boxed{\frac{5}{12} } \: \:$

so, 5/12th of the cistern filled in 1 hour

then,

$\tt{1 \: of \: cistern \: filled \: in \: \frac{1}{ \frac{5}{12}} hr} \\ \\ : \implies 1 \times \frac{12}{5} \\ \\ : \implies \frac{12}{5} \: \: \: \: \: \: \: \: \: \\ \\ : \implies 2 \frac{2}{5} hr \: \: \: \: \:$

• time taken = 2 hr 24 min

hence, both taps together filled the cistern in 2 hr 24 min

Answer 2

cistern can be filled by one tap in 8 hours and by another in 4 hours . How long will it take to fill the cistern .If both taps are opened together ?