Question

Pipe A can fill a cistern in 5 hours and pipe B in 10 hours. Both the pipes are opened together and after 2 hours pipe A is closed , how much time will the pipe B take to fill up the remaining part of a tank?​

Answer 1

Given,

• Time taken for A = 5 hours

• Time taken for B = 10 hours

Part of the tank filled by pipe A and B in 2 hours can be calculated as:

$\sf{\implies 2[\dfrac{1}{5}+\dfrac{1}{10}]}$

$\sf{\implies 2[\dfrac{10+5}{5\times 10}]}$

$\sf{\implies 2[\dfrac{15}{50}]}$

$\sf{\implies \dfrac{2\times 15}{50}}$

$\sf{\implies \dfrac{30}{50}}$

$\sf{\implies \dfrac{3}{5}}$

Therefore Remaining part can be calculated as:

$\sf{\implies 1-\dfrac{3}{5}}$

$\sf{\implies \dfrac{5-3}{5}}$

$\sf{\implies \dfrac{2}{5}}$

Therefore required time can be calculated as:

$\sf{\implies \dfrac{3}{5}\times8 }$

$\sf{\implies \dfrac{3\times 8}{5}}$

$\sf{\implies \dfrac{24}{5}}$

$\sf{\implies 4\dfrac{4}{5} \ hours}$

$\boxed{\sf{\therefore \ Required \ time= 4\dfrac{4}{5} \ hours}}$