Three taps A, B and C can fill a tank in 10, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, find the time taken to fill the tank.
Answers
Question:-
Three taps A, B and C can fill a tank in 10, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, find the time taken to fill the tank.
Solution:-
From the given information, we can have
A's 1 hour work = 1/10
B's 1 hour work = 1/15
C's 1 hour work = 1/20
In the first hour, we have
(A + B)'s work = 1/10 + 1/15
(A + B)'s work = 3/30 + 2/30
(A + B)'s work = 5/30
(A + B)'s work = 1/6
In the second hour, we have
(A + C)'s work = 1/10 + 1/20
(A + C)'s work = 2/20 + 1/20
(A + C)'s work = 3/20
Amount of work done in each two hours is
= 1/6 + 3/20
= 10/60 + 9/60
= 19/60
Amount of work done :
In the first 2 hours : 19/60
In the first 4 hours : 19/60 + 19/60 = 38/60
In the first 6 hours : 19/60 + 19/60 + 19/60 = 57/60
After 6 hours, the remaining work will be
= 3/60
= 1/20
1/20 is the small amount of work left and A alone can complete this.
Time taken by A to complete this 1/20 part of the work is
= Amount of work / Part of work done in 1 hour
= (1/20) / (1/10)
= (1/20) ⋅ (10/1)
= 1/2 hours
So, A will will take half an hour (or 30 minutes) to complete the remaining work 1/20.
So, total time taken to complete the work is
= 6 hours + 30 minues
= 6½ hrs