A and B can do a piece of work in = 40 daysB and C can do a piece of work in = 30 daysC and A can do a piece of work in = 24 days
(A+B)’s 1-day work =`1/40`
(B+C)’s 1-day work =`1/30`
(C+A)’s 1-day work =`1/24`
(i) [(A+B)+(B+C)+(C+A)]’s 1 day work = `1/4+1/30+1/24`
`=(3+4+5)/120`
`=12/120=1/10`
i.e. (A+B+B+C+C+A)'s 1-day work =`1/10`
i.e. 2 (A+B+C)'s 1-day work =`1/10`
∴ (A+B+C)'s 1-day work =`1/10xx1/2`
`=1/20`
∴ (A+B+C) can do the work in = 20 days
(ii) A's 1-day work =`1/20-1/30`
`=(3-2)/60=1/60`
∴ A can do the work in 60 days
B's 1-day work =`1/20-1/24`
`=(6-5)/120=1/120`
∴ B can do the work in 120 days
now, C's 1-day work =`1/20-1/40`
`=(2-1)/40=1/40`
C can do the work in 40 days
Hence A can do the work in = 60 days
B can do the work in = 120 days
C can do the work in = 40 days
Question 7 Time and Work Exercise 11.1
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Answer:
Every task necessitates a specific amount of time and a specific workforce, or the number of individuals who will complete the task.
Work is usually categorised as a "1" unit. This time and and work concept is a follow-up to direct and inverse proportion.
The given details are,
A and B can do a piece of work in = 18 days
Work done by A and B in 1 day = 1/18
B and C can do a piece of work in = 24 days
Work done by B and C in 1 day = 1/24
A and C can do a piece of work in = 36 days
Work done by A and C in 1 day = 1/36
By adding A, B and C we get,
2(A+B+C) one day work = 1/18 + 1/24 + 1/36
= (4+3+2)/72 (by taking LCM for 18, 24 and 36 which is 72)
= 9/72
= 1/8
A+B+C one day work = 1/(8×2) = 1/16
∴ A, B and C together can finish the work in = 1/(1/16) = 16days.
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