Working together, A and B can do a job in 6 days. B and C can do the s

Let the total work be 450 units...

So, Efficiency of A + B is 75 ; Efficiency of B + C is 45 & Efficiency of C + A is 60

Total efficiency of A + B + C is \(\frac{75 + 45 + 60}{2} = 90\)

Now, Efficiency of A is 90 - 45 = 45 , so time required is 450/45 = 10, Answer must be (B)

Given:
1. Working together, A and B can do a job in 6 days.
2. B and C can do the same job in 10 days
3. C and A can do it in 7.5 days.

Asked: How long will it take for A alone to complete the job?

Let A, B, & C complete the job alone in a,b & c days respectively

1. Working together, A and B can do a job in 6 days.
1/a + 1/b = 1/6 (1)
2. B and C can do the same job in 10 days
1/b + 1/c = 1/10 (2)
3. C and A can do it in 7.5 days.
1/c + 1/a = 2/15 (3)

Adding (1) , (2) & (3)
2(1/a + 1/b + 1/c) = 1/6 + 1/10 + 2/15 = (5+3+4)/30 = 12/30 = 2/5
1/a + 1/b + 1/c = 1/a + 1/10 = 1/5
1/a = 1/5 - 1/10
a = 10

IMO B

If they don't tell you the size of the job, that's a clue that you can choose any number you want for the size.

Choose something that will divide easily by the values in the problem (6, 10, and 7.5). A good choice would be 60. Let's say that the job is to assemble 60 puzzles.

A and B working together can assemble 60 puzzles in 6 days. So, A and B together work at a rate of 10 puzzles per day.

Similarly, B and C work together at a rate of 6 puzzles per day.

Finally, A and C work together at a rate of 8 puzzles per day.

We'd like to know A's rate. Let A = A's rate per day, B = B's rate per day, and C = C's rate per day.

A + B = 10
B + C = 6
A + C = 8

Combine the second two equations:

(A + C) - (B + C) = 8 - 6

A - B = 2

Combine this with the first equation:

A + B = 10
A - B = 2

2A = 10 + 2 = 12

A = 6

So, A assembles 6 puzzles per day. (At this point, you can plug this back in to the info you know thus far in order to double check your math - I did!)

At a rate of 6 puzzles per day, it will take A 10 days to assemble 60 puzzles, so the answer is B.