If A and B work together, they will complete a job in 7.5 days. Howeve

A and B together can complete the job in 7.5 days. If A do half of the jobs then B do half of the jobs they can complete in 20 days.

If we take multiplication of 7.5 and 20 = 150 as total work.

Then combine work in one day is = 150/7.5=20, A is more efficient than B, so if we consider A is doing 15 while B is doing 5(randomly easy to work, ball parking).

so total job we have considered = 150, half the job = 75.

A do half the job in 75/15 = 5 days
B do half of the jobs in 75/5 = 15 days.

Which satisfy with the statement that, after half done by A, B do half and complete in 20 days.

So B can do the entire job in 150/5 = 30 days

In this problem, any algebraic solution would involve a quadratic equation, factorization etc hence time-consuming. Using the answer choices is a much quicker option:
Let 'x' and 'y' be the number of days needed by A and B respectively to do the job alone. Then A does half the job in x/2 days and B the remaining half in y/2 days. (x/2+y/2)=20...> x+y=40.....(i)
Working together, A and B can finish the job in 7.5 days. Therefore:
7.5 (1/x + 1/y) = 1...> {7.5(x+y)/xy}=1...> 7.5*40=xy...> xy=300.....(ii)
Answer Option (A): If 'y' (days needed by B to do the job alone) is 20 'x' is also 20, xy=400 so NO.
Option (B): If 'y' is 24 'x' is 16, xy=384. NO
(C): y=30, x=10. YES. ANS:C

Solving through options
Starting with the middle one. Lets assume B alone takes 30 days. Then it would take B 15 days to finish half the work. So first half must have been already done by A in 5 days (since they take 20 days to finish half thw work one by one)

Now using this information to verify the data when they work together. Working alone A should take (5×2) 10 days. And we know B takes 30 days (assumption)
At this rate working together they should take 7.5 days. (Matches with the info given to us)

Hence option C

If you have time you can also sww why other options are wrong

A. Assuming B takes 20 days. Half work = 10 days. This means first half for A is also 10 (not possible since A is more efficient)
B. Assuming B takes 24 days. Half work = 12 days. Half work for A is then 8 days. That means A shud take 16 days to complete. Together they wont be taking 7.5 days

And so on

Posted from my mobile device

note that only option C is a multiple of 7.5
rate of A+B working together=1/(7.5)=4/30
if A is more efficient than B,
then A's rate=3/30 and B's rate=1/30
1/30+3/30=4/30
30 days
C

Hi Team,

Quick question on my side.

When I tried to resolve this problem, I did the following :

First information given : 1/A + 1/B = 7.5 = 2/15

Second information given 1/2A + 1/B = 1/20

Then, First information - Second information = 1/A - 1/2A + 1/B - 1/B = 2/15 - 1/20. That gave me A = 6.

Therefore, 1/6 + 1/B = 2/15, meaning 1/B = -1/30. I knew that "B" couldn't be <0 but I still picked "C" as an answer because the denominator was equal to 30.
Can someone explain to me what did I do wrong I just can't get my head around it.
Thanks !

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