Question

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

Answer 1

Step-by-step explanation:

They can finish it alone as A in 40 days , B in 60 days and C in 120 days.

Step-by-step explanation:

Given : 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.

To find : In what time can each finish it working alone?

Solution :

According to question,

A + B = 40 days

B + C = 30 days

C + A = 24 days

We take the LCM of 24,30 and 40

2 | 24 30 40

2 | 12 15 20

2 | 6 15 10

3 | 3 15 5

5 | 1 5 5

| 1 1 1

LCM(24,30,40)=2\times 2\times 2\times 3\times 5LCM(24,30,40)=2×2×2×3×5

LCM(24,30,40)=120LCM(24,30,40)=120

Their unit work in a day will be

A + B = \frac{120}{40}=3

40

120

=3 units/day

B + C = \frac{120}{30}=4

30

120

=4 units/day

C + A = \frac{120}{24}=5

24

120

=5 units/day

Adding these equations ,

2A + 2B + 2C = 3+4+5

2(A + B + C) = 12

A + B + C = 6 units per day

Now, to complete 120 units they'll take a time of

t=\frac{120}{6}t=

6

120

t=20t=20

Together they take A+B+C= 20 days.

So, they working alone as

For A,

A's one day work is 6-3=3 unit

A complete whole work in \frac{120}{3}=40

3

120

=40 days

For B,

B's one day work is 6-4=2 unit

B complete whole work in \frac{120}{2}=60

2

120

=60 days

For C,

C's one day work is 6-5=1 unit

C complete whole work in \frac{120}{1}=120

1

120

=120 days

Therefore, they can finish it alone as A in 40 days , B in 60 days and C in 120 days.

# Learn more

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

https://brainly.in/question/12464579