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. in what time can each finish it working alone?

Answer 1

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

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

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

Their unit work in a day will be

A + B = $\frac{120}{40}=3$ units/day

B + C = $\frac{120}{30}=4$ units/day

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

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

$t=20$

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 $\frac{120}{3}=40$ days

For B,

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

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

For C,

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

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

Answer 2

Answer:

i)20 days

ii) A=60 days

B=120 days

C=40 days

Step-by-step explanation:

i) (3+4+5)/120=12/120=1/10

(A+b+c+a+b+c) 1 day work =1/10

(A+B+C) =1/10×1/2=1/20

=20 days

ii) A work = 1/20-1/30

(3-2)/60 = 1/60=60 days

B work =1/20-1/24

(6-5)/120=1/120=120 days

C work=1/20-1/40

(2-1)/40=1/40=40 days