Answer
It took both Pipes A & B $8\frac{4}{7}$ days to fill up the pond.
Work Step by Step
Let $x$ days be the time needed to fill up the pond by both of the pipes together, and $C$ be the total capacity of the pond
The capacity of the pond to be filled by Pipe A alone in 1 day is $\frac{1}{20}C$
The capacity of the pond to be filled by Pipe B alone in 1 day is $\frac{1}{15}C$
The capacity of the pond to be filled by both of the Pipes A & B in 1 day is $\frac{1}{x}C$
Therefore,
$\frac{1}{20}C$ + $\frac{1}{15}C$ = $\frac{1}{x}C$
$\frac{1}{20}$ + $\frac{1}{15}$ = $\frac{1}{x}$
$\frac{15 + 20}{300}$ = $\frac{1}{x}$
$35x = 300$
$x = \frac{300}{35}$
$x = \frac{60}{7}$
$x = 8\frac{4}{7}$
Hence, it took both Pipes A & B $8\frac{4}{7}$ days to fill up the pond.
