Because after years of this tests I developed an instinct.

C is the standard formula for the work combined. Out. The pumps are not aligned

E has no sense because B has to catch up A not the other way around

D has no sense the - 1 at post of the fraction

A We do know that the numerator must be a multiplication, not a sum.

B is left.

These are sorts of a thing you have after years. You suddenly know what is wrong. It is something in your mind. 8000 kudos on gmatclub and now here since 2 years......well, they need for something

We can let the rate of pump A = 1/A and the rate of pump B = 1/B.

We can let the time of pump A = T and the time of pump B = T - 1.

We will use the equation for work to answer the question: work = rate x time. We sum the individual work of pumps A and B, and they perform 1 job, which is to empty the entire pool. Thus, we create the following equation:

(1/A)(T) + (1/B)(T - 1) = 1

T/A + (T - 1)/B = 1

Multiplying by AB, we have:

TB + TA - A = AB

TB + TA = AB + A

T(B + A) = AB + A

T = (AB + A)/(B + A)

T = A(B + 1)/(B + A)

Answer: B

Choose a random number for a and b suppose A=10 and B=5

A can do 1/10 work in 1 min
B can do 1/5 work in 1 min

There is 1 work to do. Since A comes in and does 1/10 work by working alone for 1 min
The remaining work is 10/10-1/10=9/10
If A and B work together they can do 15/50 work in 1 min so they will take 50/15 minutes to complete the total work
However they only have to do 9/10 of the total work so they can complete the total work in 50/15* 9/10 = 3 mins
total time taken 1 min for A and 3 min for A+B = 4 minutes

Replace the value of A=10 and B=5 in the answer choices option B gives 4
This process can take more than 2 minutes but it is just another way of solving the question

Try it this way: