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RD Sharma Solutions Class 8 Mathematics Solutions for Time and Work Exercise 11.1 in Chapter 11 - Time and Work
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A, B and C working together can do a piece of work in 8 hours. A alone can do itin 20 hours and B alone can do it in 24 hours. In how many hours will C alone dothe same work?
The given details are,
A can do a piece of work in 20 hoursWork done by A in 1 hour = 1/20
B can do same work in = 24 hours Work done by B in 1 hour = 1/24
A, B and C working together can do the same work in = 8 hours
Work done by A, B, C together in 1 hour = 1/8
We know that,
Work done by C in 1 hour = (work done by A,B and C in 1 hour) – ( work done by A And B in 1 hr.)
= 1/8 – (1/20 + 1/24)
= 1/8 – 11/120
= (15-11)/120 (by taking LCM for 8 and 120 which is 120)
= 4/120
= 1/30
∴ Time taken by C alone to complete the work = 1/(1/30) = 30hours.
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