Question

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 ?​

Answer 1

1)15days is our correct answer

Answer 2

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 =  $\frac{1}{40}$

Work done by B & C in one day =  $\frac{1}{30}$

Work done by C & A in one day =  $\frac{1}{24}$

Work done by A, B, C working together =

2 ( A + B +C ) = $\frac{1}{40}$ + $\frac{1}{30}$ + $\frac{1}{24}$

⇒ 2 ( A + B +C ) = $\frac{21}{120}$

⇒ A + B +C = $\frac{21}{240}$

⇒ A + B +C = $\frac{7}{80}$

This is the work done by A, B & C working together.

Now total time taken by A, B & C working together = $\frac{80}{7}$ = 11.42 days

(2). Work done by C in one day = $\frac{7}{80}$ - $\frac{1}{40}$

⇒ $W_{C} = \frac{1}{16}$

⇒ Thus time taken by C to complete the work = 16 days

Work done by A in one day = $\frac{7}{80}$ - $\frac{1}{30}$

⇒ $W_{A}$ = $\frac{13}{240}$

⇒ Time taken by A to complete the work = $\frac{240}{13}$

⇒ Thus time taken by A to complete the work = 18.46 days

Work done by B in one day = $\frac{7}{80}$ - $\frac{1}{24}$

⇒ $W_{B}$ = 0.0458

⇒ Time taken by B to complete the work = $\frac{1}{0.0458}$

⇒ Thus time taken by B to complete the work = 21.83 days