Question

Three taps can fill a tank in 4,6 and 8 hours. if they are opened one after another for one hour each,starting with the first tap how much they will altogether take to fill a cistern

Answer 1

So, as per the question,

Tap A fills the tank in 4 hours,

So, in one hour it will fill 1/4 th part of tank

Similarly, Tap B fills 1/6th part of tank in 1 hour

Tap C fills 1/8th part of tank in 1 hour

Now,

As the Taps are included in for a interval of 1 hours;

So, for the first three hours the part of tank filled is;

=1/4 + 1/6 + 1/8

=10 /24 + 1 / 8

= 13/24

13/24th part of tank is filled

Now, when Tap A is on for the second time,

=13/24 + 1/4

=(13 + 6)/24

=19/24

When Tap B is on for the second time,

=19 /24 + 1/6

=(19+4)/24

=23/24

Now for Tap C let us assume it was on for x amount of time

So,

23/24 + x/8 = 1 (1 means that the tank is full)

x/8 =1 - 23/24

x/8=1/24

x = 1/3

=(60 / 3) =20 min

So,

Total time taken is

(3 + 1 + 1 ) + 20min

=5 hours 20 min

So,

it will take

5 hours 20 min to fill the tank