Question : Pipes A, B, and C can fill a tank in 15, 30 and 40 hours, respectively. Pipes A, B, and C are opened at 6 a.m., 8 a.m., and 10 a.m. on the same day. When will the tank be full?
Option 1: 3:20 p.m.
Option 2: 11:20 p.m.
Option 3: 7:20 p.m.
Option 4: 5:20 p.m.
Correct Answer: 3:20 p.m.
Solution :
Let the total work = LCM of 15, 30, and 40 = 120 units
Efficiency of A = $\frac{120}{15}$ = 8
Efficiency of B = $\frac{120}{30}$ = 4
Efficiency of C = $\frac{120}{40}$ = 3
According to the question,
From 6 am to 8 am, work done by A = 2 × 8 = 16 units
From 8 am to 10 am, work done by A and B = 2 × 12 = 24 units
⇒ Remaining work = 120 – 16 – 24 = 80 units, A, B and C completed together
⇒ Time taken by A, B, and C to finish the remaining work = $\frac{80}{8+ 4+ 3}$ = $5\frac{1}{3}$ = 5 hours 20 minutes
So, the tank fills at 10 am + 5 hours 20 minutes = 3:20 p.m.
Hence, the correct answer is 3:20 p.m.
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