Question

A water pump takes 6 hours to fill an over head tank.standby pump takes 10 hours

Answer 1

What is the question here

Answer 2

The stand by tank will take the time of 6 hours and 40 mins

Given:

Time taken by water pump = 6 hours

Time taken by standby pump = 10 hours  

To find:

Time taken by standby pump  to fill the rest of tank  

Solution:

The first pump fails after 2 hours  

We have been given the information that the 'water pump' takes 6 hours to fill a tank. Hence, the proportion of tank filled in 1 hour will be as

1 hour $=\frac{1}{6}$ of the tank

If in 1 hour, the amount of tank filled is 1/6th of total tank, then the amount of water filled after 2 hours will be:

2 hours $=\frac{1}{6} \times 2=\frac{1}{3}$ of the tank

If the total proportion of tank filled as 1, then the amount of water to be filled:

Amount of water to be filled by the stand by pump

= 1 - the proportion of tank filled by water pump in 2 hours

= 1 - $\frac{1}{3}$

= $\frac{2}{3}$ of the tank

It is given that the standby pump takes 10 hours to fill the tank

1 tank = 10 hours

Hence, the number of hours required vy the standby pump to fill the rest of the tank will be as under:

$\frac{2}{3}$of the tank $= \frac{2 \times 10}{3}=\frac{20}{3}$hours = 6 hours 40 minutes

Hence, the stand by tank will take the time of 6 hours and 40 mins to fill the balance  proportion of the tank.