# A and B Can Do a Piece of Work in 40 Days; B and C in 30 Days; and C and a in 24 Days. (I) How Long Will It Take Them to Do the Work Together? (Ii) in What Time Can Each Finish It Working Alone? - Mathematics

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Sum

A and B can do a piece of work in 40 days; B and C in 30 days; and C and A in 24 days.
(i) How long will it take them to do the work together?
(ii) In what time can each finish it working alone?

#### Solution

A and B can do a piece of work in = 40 days
B and C can do a piece of work in = 30 days
C 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

Concept: Time and Work
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Chapter 10: Direct and Inverse Variations - Exercise 10 (E) [Page 133]

#### APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 10 Direct and Inverse Variations
Exercise 10 (E) | Q 14 | Page 133
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