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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 basic concept of time and work is similar to that across all arithmetic topics, i.e., the concept of proportionality.

Efficiency is inversely proportional to the time taken when the amount of work done is constant.

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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