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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 8 Time and Work Exercise 11.1

A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20days. How much time will A alone take to finish the work?

Answer:

The given details are,

A and B can do a piece of work in = 12 days

Work done by A and B in 1 day = 1/12

B and C can do a piece of work in = 15 days

Work done by B and C in 1 day = 1/15

A and C can do a piece of work in = 20 days

Work done by A and C in 1 day = 1/20

By adding A, B and C we get,

2(A+B+C)’s one day work = 1/12 + 1/15 + 1/20

= (5+4+3)/60 (by taking LCM for 12, 15 and 20 which is 60)

= 12/60

= 1/5

A+B+C one day work = 1/(5×2) = 1/10

We know that,

A’s 1 day work = (A+B+C)’s 1 day work – (B+C)’s 1 day work

= 1/10 – 1/15

= (3-2)/30 (by taking LCM for 10 and 15 which is 30)

= 1/30

∴ A alone can finish the work in = 1/(1/30) = 30days.

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