Question

Taps A B and C can fill a tank in 10 hours, 12
hours and 15 hours respectively. An outlet pipe
can empty the tank in 5 hours. The three taps
and the outlet were opened and allowed to run
for 5 hours after which the outlet was closed.
How long will it take the three taps to fill the
remaining tank
​

Answer 1

Answer:

Work done by X in 1 hr = 1/10

Work done by Y in 1 hr = 1/12

Work done by Z in 1 hr =1/15

Work done by outlet pipe in 1 hr = -1/5(empty the full tank-so we take the work as negative)

Let the outlet pipe be 'O'

Work done by ( X + Y +Z ) in 5 hrs.=

=5(1/12 + 1/10 + 1/15)

=5(5+6+4/60)

=5+6+4/12

=15/12

But for the first 5 hrs. the outlet pipe was also opened

hence total tank filled in 5 hrs. =

= 15/12 - 1

( we substracted one beacuse '1' is the amount of work done by the outlet pipe in 5 hrs. .i.e. -1/5 * 5= -1    It's the same as we have done for the pipes X Y and Z in the 5 hrs. )

=15-12/12

=3/12

=1/4

Hence the amount of tank filled in 5 hrs. is 1/4

Now the outlet valve has been closed

hence amount of tank left to be filled = 3/4

now let the time that is taken by taps to fill the rest of the tank is 'a'

therefore

3/4 = a ( 1/10 + 1/12 + 1/15 )

(because we needed to multiply the one hours work with time taken to fill 3/4 of the tank)

3/4 = a (15/60)

3/4 = a (1/4)

hence on solving we have

a = 3 hrs.

therefore total time taken by the three taps and the outlet to fill the tank is 8 hrs.

and after closing the outlet the total time taken by taps to fill leftover tank is 3 hrs.

HOPE THIS HELPS

Answer 2

Answer:

a=3 hours

Taps A B and C can fill a tank in 10 hours, 12

hours and 15 hours respectively. An outlet pipe

can empty the tank in 5 hours. The three taps

and the outlet were opened and allowed to run

for 5 hours after which the outlet was closed.

How long will it take the three taps to fill the

remaining tank