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RD Sharma Solutions Class 8 Mathematics Solutions for Time and Work Exercise 11.1 in Chapter 11 - Time and Work

Question 6 Time and Work Exercise 11.1

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?

Answer:

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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