Question

An empty tank is connected with pipes A, B and C. A and B inlet pipes and they fill the tank in $6$ hours and $8$ hours respectively. While C is an outlet pipe and it empties the completely filled tank in $5$ hours. Find the time in which the tank will be completely filled if all the pipes are opened together.

• A. $\frac{119}{11}$ hours
• B. $\frac{108}{11}$ hours
• C. $\frac{120}{11}$ hours
• D. $\frac{109}{11}$ hours

Answer 1

Answer: (C)

$\frac{120}{11}$ hours

Work rate of Pipe A = 100/6 = 16.66 % per hour
Work rate of Pipe B = 100/8 = 12.5 % per hour
Work rate (Negative) of Pipe C = 100/5 = 20% per hour
So, Combined work rate of A, B and C
= 16.66 + 12.50 - 20 = 9.16 % per hour
Time taken to fill the tank = 100/9.16 = 10.9 hours = 120/11 hours.
Alternatively you can solve it through fractional method as well,
A fills = 1/6 part per hour
B fills = 1/8 part per hour
C empties = 1/5 part per hour
Combined work
= 1/6 + 1/8 - 1/5
=(20 + 15 - 24) / 120 = 11/120 part per hour
Time taken to completed the work = 120 / 11 hours.