Question

If a pipe can fill the tank in 6 hrs but unfortunately there was a leak in the tank due to which it took 30 more minutes .now if the tank was full how much time will it take to get emptied through the leak?

Answer 1

Rate of volume with which liquid is filled is let say Q

now if it is filled in 6 hours then

total volume of the container will be

$V = Q*6$

let the flow rate at which the liquid is flowing out is Q'

so net flow rate inside the container will be

$Q_{net} = Q - Q'$

now the total time to fill the container will be 6.5 hours

so total volume will be

$V = (Q - Q')*6.5$

now by above two equations we have

$Q*6 = (Q - Q')*6.5$

$6.5*Q' = 0.5*Q$

$Q' = \frac{Q}{13}$

now time to complete drain out of the liquid is "t"

so we will have

$Q'*t = V$

$\frac{Q}{13}* t = Q*6$

$t = 13*6 = 78 hours$

so it will take 78 hours for complete drain out of the container

Answer 2

Answer:

78 hours

Explanation:

tank filling rate = 1/6 per hour

time taken with leakage = 6 1/2 = 13/2 hrs

tank filling rate with leakage = 2/13 per hour

therefore, rate of leakage = 1/6-2/13 = 1/78

hence, it will take 78 hours to empty the tank, if the tank is full.