Three pipes A, B and C can fill a tank in 6 hours. After working together for 2 hours, C is closed while A and B fill the remaining part in 7 hours. In how many hours can C alone fill the whole tank?
Three pipes A, B and C can fill a tank in 6 hours. After working together for 2 hours, C is closed while A and B fill the remaining part in 7 hours. In how many hours can C alone fill the whole tank?
Options
- a.
15
- b.
16
- c.
12
- d.Correct answer
14
Explanation
A, B, C finish 42 work in 6 hrs.
i.e. A, B, C 1 hr work = 42/6 = 7 work
A, B, C = 2 hr work = 2 × 7 = 14 work
Out of 42 work, ABC finish 14 work in 2 hrs.
Remaining work = 42 – 14 = 28 work Completed by A & B together in 7 hrs.
A & B finish 28 W in 7 hrs.
A, B 1hr work 28/7 = 4 work
Initially in 2 hrs, A & B also working.
In 2 hrs, A & B finish = 2 × 4 = 8 Work
Total from beginning to end, A & B finish 8 + 28 = 36 work completed by A & B
Out of 42 work, A & B alone finish 36 work and left out work (42 – 36 = 6 work) completed by C in 2 hrs.
C in 2 hrs. = 6 work
i.e. 6 work by C = 2 hrs.
Total Work 6 × 7 = 42 work by C in 2 × 7 = 14 hrs.
C alone finish entire work in 14 hrs.
Ans Option ‘d’
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