Question

pipes a and b can fill a tank in 5 and 6 hours respectively. Pipe c can empty it in 12 hours. The tank is half fill. All 3 pipes are in operation simultaneously. After how much time will the tank be full

Answer 1

(1/5)+(1/6)-(1/12) = (12+10-5)/60
17/60
by doing reciprocal we get
60/17 hours

Answer 2

time taken to fill the tank in 1 hr = 1/5+1/6=11/30hrs..
to empty the tank in 1hr=1/12 hr
to fill the tank by A,B,C= 11/30-1/12=17/60 =60/17 hrs or 3(9/17)hr
OR
using LCM method to solve this problem,

A --- 5
B --- 6
C --- -12
for total Capacity, take the LCM of 5,6,12 that is 60
Now per hour capacity of A= 60/5 = 12
per hour capacity of B= 60/6 = 10
per hour capacity of A= 60/-12 = -5

thus per hour capacity of A+B+C = 12+10-5 = 17
thus total time = total capacity/ per hour capacity = 60/17 hours