Method 1:  Using variables

Let the no of pipes be x.

Number of pipe days needed to fill tank A is $\frac{x}{2}+\frac{x}{4}$
This is double the amount taken to fill tank B....
The equations is,$\frac{\frac{x}{2}+\frac{x}{4}}{2}=(\frac{x}{4}+1)$

Thus, x=4.

Method 2: Using numbers (Assumption)

Assume answer to be option (b) - a middle answer option

Let A have a capacity of 300 litres

B will have a capacity 150 litres

Now 4 pipes fill A for half a day = effectively 2 pipes working for an entire day = 100 litres are filled by the first half

And 2  pipes fill A for another half = effectively 1 more pipe fills A for an entire day

This means that 3 pipes fill A completely= 300 litres

Thus, each pipe fills 100 litres

Let us verify it with B

Given that in the first day, 2 pipes fill B for half a day $\Rightarrow$ one pipe fills B for an entire day = 100 litres

Now 50 litres is left which Is filled by one pipe in half a day.
TOTAL = 150 litres for B

Thus, our assumption is correct