Question

In a tank there are four outlets A B cans D these outlets can empty the tank in 10 min 12 min 15 min and 18 min if the tank is full and all the outlets are opened how much time will it take to empty the whole tank if the outlets A B are closed after 1 min and 2 min respectively and the C is closed 5 mins before the tank gets empty

Answer 1

Answer:

ABCD all together

1/10 + 1/12 + 1/15 + 1/18 = (18+15+12+10)/180

= 55/180

= 11/36

Or 36/11 = 3.272 minutes

Water emptied by A

= 1/10

Water emptied by B

= 2*1/12

= 1/6

Now,

As per the question

1/10 + 1/6 + (t-5)/15 + t/18 = 1

(t-5)/15 + t/18 = 1-1/10-1/6

(t-5)/15 + t/18 = 9/10-1/6

(t-5)/15 + t/18 = (54-10)/60 = 44/60 = 11/15

t/15 + t/18 = 11/15 + 5/15

t/15 + t/18 = 16/15

t(6+5)/90 = 16/15

t = 16*90/15*11

t = 96/11 = 8.727 minutes