P= Q+5
PQ/P+Q (combined filling time)
= 6
Upon substitution Q^2-7x-30.
Q=10, P=15

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can someone explain this question, I am unable to get the right answer

Hey sthahvi,

I'm happy to give it a try.

In this situation, I think the easiest way to solve this question is by using the different answers.

First thing first, it is said that : P and Q running together take 6 minutes -> 1/P + 1/Q = 1/6

Then, it is said that : P takes 5 more minutes than Q to do the job. Then, P = Q + 5 -> 1/Q+5 + 1/Q = 1/6

From here, you have 2 options : either you develop the equation 1/Q+5 + 1/Q = 1/6 to form a polynomial equation (which I think is the longest option) OR you use the different answers that you are provided with :

We know that P takes 5 minutes longer than Q, so you can straight away get rid of answers A, C and E.

Then, plug the numbers from B and D into the equation :

If you use answer B it gives you :
1/15 + 1/10 = 2/30 + 3/30 = 5/30 = 1/6 -> Bingo !

I hope it helps,

Answer : B.