t1 time the first pipe takes to fill the tank
t2 time the second pipe takes to fill the tank
t3 time the third pipe takes to fill the tank


We know that pipes 1 and 2 operating simultaneously take the same time to fill the tank as pipe 3 operating alone,

so:


1/t1 +1/t2 =1/t3

We also know that pipe 2 fills the tank 5 hours faster than pipe 1: t2= t1 - 5

And pipe 2 is 4 hours slower than the pipe 3: t3= t2-4


So we have the following relationships:

t1

t2= t1-5

t3=t2-4= t1-9


If we try the diferent solutions proposed, we find that Answer C is the correct answer with t1=15; t2=10 and t3= 6


1/15 + 1/10 =5/30 =1/6 (1/t3= 1/t1+1/t2)