Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. Th

hi Bunuel,
THanks for such a lovely Q.. Edited

The answer is given as D. I think you should check the highlighted part.

Answer is (D)
A does 1/a part in 1 day =2/a part in 2 days
Similarly B does 2/b part is 2 days
When A starts
2/a+2/b+2/a+2/b+2/a=1 => 6/a+4/b=1 .....................(1)

When B starts
2/b+2/a+2/b+2/a+2/b+1/2a(Half days work) =1 => 2/b=3/2a ..................(2)

Solving (1) and (2)
we get a=9 and b = 12

A and B together does the work in ab/a+b =108/21 =36/7 days

Hence Answer is (D)

equation1: 6/a+4/b=1
equation2: 9/a+12/b=2
solving, a=9;b=12
let d=days for A and B to complete task working together
d(1/9+1/12)=1
d(7/36)=1
d=36/7 days

So I started and got the following equation, would love to get help on where I have gone wrong
6/a + 4/b = 1/10
That is 6 * 1/a (rate of A) and 4 * 1/b (rate of B) = 1/ 10 (overall time utilised)

second equation followed the same route, is my equation wrong??

When A starts, A works for 6 days and B for 4 days to complete the work.
6/a + 4/b = 1 Work

When B starts, A works for 4.5 days and B for 6 days to complete the work.
4.5/a + 6/b = 1 Work

Solving these two equations simultaneously, we get:
18/a + 12/b = 3
9/a + 12/b = 2
9/a = 1
a = 9
b = 12

Rate of work while working together = 1/9 + 1/12 = 7/36
Time taken to complete the work = 36/7 days
Answer (D)

Let their efficiency ratio be a:b
Therefore, 6*a+4*b=4.5*a+6*b
=>a to b is 4:3
Number of days taken will be 3*k and 4*k, where k is a constant.
If they work together they take (3*k)*(4*k)/3*k+4*k = 12*k^2/7*k = 12*k/7
Look at the option. Only D could be the correct one.

Q. Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?

Sol: The rate of work and all the fractions might look a little confusing, so I tried to break it down in simple terms.

Scenario 1 - A starts and proceeds to work for two days, followed by B who also works for 2 days. In this case, the work is completed in 10 days. Which means A has worked for 6 days and B has worked for 4 days (A,A,B,B,A,A,B,B,A,A).

Scenario 2 - B starts and proceeds to work for two days, followed by A who also works for 2 days. In this case, the work is completed in 10.5 days. Which means A has worked for 4.5 days and B has worked for 6 days.

Now, if we equate both scenarios, we get - 6A + 4B = 4.5A + 6B. Solve the equation and you get - A:B = 2:1.5 (or 4:3).

Since we have the ratio of their efficiencies, we can use the same get an estimate of the work done. For eq, since the ratio of their efficiencies is 4:3, we can go ahead with the assumption that A has done 4 unites of work per day, while B has done 3 units of work per day. Substitute these values in one of the scenarios, and you get the total work done.

6A + 4B (scenario one) can be written as 6*4 + 4*3 = 36. Now, that we have the total work, simply divide this by the work that can by A & B in a day if they work together, which is 4+3 = 7.

Now, to find the number of days required to complete the task if they both work together, we just have to divide the total work by the work that can by A & B in a day if they work together => 36/7

I tried to make it as elaborate as possible to make it easier to understand each step, so that it'll be easier for you to remember and replicate. Once you get a hang of it, this should not take more than a minute to solve.