Pipes A and B can fill a tank in 4 hours and 6 hours 40 minutes, respectively, whereas a third pipe C can empty the full tank in 1 hour 40 minutes. A and B are opened at 2:00 p.m., 3:00 p.m., respectively and C is opened at 4:00 p.m. The tank will be completely empty at:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 7:15 p.m.
A fills in 4 hrs , so Efficiency of A = 1/4
B fills in 6h 40m = 20/3 hrs, so efficiency of B = 3/20
C empties in 1h 40m = 5/3 hrs , so efficiency of C = −3/5
2:00–3:00 p.m. , Only A , Filled=1/4
3:00–4:00 p.m. , (A + B) = (1/4) + (3/20) = 2/5
Total filled by 4:00 =(1/4) + (2/5) = 13/20
After 4:00 p.m., A + B + C = (1/4) + (3/20) − (3/5) = − 1/5
Time to empty 13/20 at 1/5 efficiency = (13/20) ÷ (1/5) = 65/20 = 3.25 hrs = 3 hrs 15 mins
Final time = 4:00 + 3:15 = 7:15 p.m.