Question

Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in:
A.6 hours
B.62/3 hours
C.7 hours
D.71/2 hours

Answer 1

Answer:

C. 7 hrs

Step-by-step explanation:

A's 1 hr work = 1/12

B's 1 hr work = 1/15

C's 1 hr work = 1/20

(A+B)'s 1 hr work  = (1/12)+ (1/15) = 3/20

(A+C)'s 1 hr work = (1/12) + (1/20) = 2/15

Now work completed in first two hrs = (3/20) + (2/15) = 17/60

Now work completed in next two hrs = 2 * (17/60) = 17/30

Now total Time taken  = 4 hrs

Now work completed in next two hrs = 2 * (17/30) = 17/15

Total time taken = 6 hrs,

Now work Remaining = 1- (17/15) = -2/15

So in next one hour pipes (A+C) work will fill the tank = 2/15-2/15

                                                                                         = 0

So Total time take to fill the tank is 7 hrs