Question

A cistern can be filled by one tap in 8hours and by another in 4hours. In how much time will a cistern be filled. If both taps are opened together

Answer 1

Answer: Both the tap if kept open then the cistern will be filled up in 8/3 hr.

Step-by-step explanation:

Shown in picture......

Answer 2

If both taps are opened together, the cistern will be filled in $\frac{8}{3}$ hours

Solution:

Given that,

A cistern can be filled by one tap in 8 hours

In, 1 hour, the tap fills 1/8 of the cistern

A cistern can be filled by another tap in 4 hours

In, 1 hour, the tap fills 1/4 of cistern

Therefore, together they can fill tank in:

$\rightarrow \frac{1}{8} + \frac{1}{4}\\\\\rightarrow \frac{1 \times 4}{8 \times 4} + \frac{1 \times 8}{4 \times 8}\\\\\rightarrow \frac{ 4 + 8}{32}\\\\\rightarrow \frac{12}{32} = \frac{3}{8}$

So they filled 3/8 of the cistern in 1 hour

So, They both filled whole cistern in 8/3 hours

Thus, if both taps are opened together, the cistern will be filled in $\frac{8}{3}$ hours

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