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,
working together?
(ii) In what time can each finish it working alone ?
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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,
working together?
(ii) In what time can each finish it working alone ?
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Total time taken by A, B & C working together = 11.42 days
Time taken by A to complete the work = 18.46 days
Time taken by B to complete the work = 21.83 days
Time taken by C to complete the work = 16 days
Step-by-step explanation:
(1). Work done by A & B in one day = [tex]\frac{1}{40}[/tex]
Work done by B & C in one day = [tex]\frac{1}{30}[/tex]
Work done by C & A in one day = [tex]\frac{1}{24}[/tex]
Work done by A, B, C working together =
2 ( A + B +C ) = [tex]\frac{1}{40}[/tex] + [tex]\frac{1}{30}[/tex] + [tex]\frac{1}{24}[/tex]
⇒ 2 ( A + B +C ) = [tex]\frac{21}{120}[/tex]
⇒ A + B +C = [tex]\frac{21}{240}[/tex]
⇒ A + B +C = [tex]\frac{7}{80}[/tex]
This is the work done by A, B & C working together.
Now total time taken by A, B & C working together = [tex]\frac{80}{7}[/tex] = 11.42 days
(2). Work done by C in one day = [tex]\frac{7}{80}[/tex] - [tex]\frac{1}{40}[/tex]
⇒ [tex]W_{C} = \frac{1}{16}[/tex]
⇒ Thus time taken by C to complete the work = 16 days
Work done by A in one day = [tex]\frac{7}{80}[/tex] - [tex]\frac{1}{30}[/tex]
⇒ [tex]W_{A}[/tex] = [tex]\frac{13}{240}[/tex]
⇒ Time taken by A to complete the work = [tex]\frac{240}{13}[/tex]
⇒ Thus time taken by A to complete the work = 18.46 days
Work done by B in one day = [tex]\frac{7}{80}[/tex] - [tex]\frac{1}{24}[/tex]
⇒ [tex]W_{B}[/tex] = 0.0458
⇒ Time taken by B to complete the work = [tex]\frac{1}{0.0458}[/tex]
⇒ Thus time taken by B to complete the work = 21.83 days