Question

3.
A and B can finish a piece of work in 30 days, B and C in 40 days while C and A in 60 days. How long will
they take to finish it together?
(1) 26 2/3days
(2) 16 2/3days
(3) 25 days
14) 24 days
(5) None of these
​

Answer 1

Answer:

a + b can do 1/30 of the job in 1 day.

b + c can do 1/40 of the job in 1 day.

a + c can do 1/60 of the job in 1 day.

We’ll represent this with:

a + b = 1/30

b + c = 1/40

a + c = 1/60

We’ll combine the first 2 lines and use the rules of algebra:

a + b + b + c = 1/30 + 1/40

2b + a + c = 7/120

2b + 1/60 = 7/120

2b = 5/120

b = 5/240

So b can do 5/240 of the job by themselves on their own in 1 day. We’ll substitute this into the first line.

a + b = 1/30

a + 5/240 = 1/30

a = 3/240

Similarly, a can do 3/240 of the job by themselves on their own in 1 day. Substitute into the 3rd line.

a + c = 1/60

3/240 + c = 1/60

c = 1/240

Thus, all 3 can do a + b + c = 9/240 of the job in 1 day.

It would take, then, 240/9 days, or 26 2/3 (27 rounded up) days to complete the job.