1. 

Two taps A and B, when opened together, can fill a tank in 6 hours. How long will it take for the pipe A alone to fill the tank?

I. B alone takes 5 hours more than A to fill the tank.

II.The ratio of the time taken by A to that taken by B to fill the tank is 2 : 3.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer

Answer: Option C

Explanation:

(A + B)'s 1 hour filling work = 1/6.

I. Suppose A takes x hours to fill the tank.

Then, B takes (X + 5) hours to fill the tank.

(A's 1 hour work) +(B's 1 hour work)
= (A + B)'s 1 hour work.

1+1=1
x(x + 5) 6

(x + 5) + x=1
x(x + 5)6


 x2 - 5x  = 12x +30

 x2 - 7x  - 30 = 0

 x2 - 10x + 3x  - 30 = 0

 x (x -10) + 3 (x - 10) = 0

 (x - 10)(x + 3) = 0

 x = 10.    [neglecting x = -3]

So, A alone takes 10 hours to fill the tank.

II. Suppose A takes 2x hours and B takes 3x hours to fill the tank. Then,

1+1=1
2x3x  6

1+1  1/ x =  1
23 6


<=> x = 5.

So, A alone takes (2 X 5) = 10 hours to fill the tank.

Thus, each one of I and II gives the answer.

 Correct answer is (C).