Two inlet pipes can fill a cistern in 5 and 6 hours respectively and an outlet pipe can empty 24 gallons of water per hour. All the three pipes working together can fill the empty cistern in 10 hours. What is the capacity (in gallons) of the tank?

Let the outlet pipe empty the completely full cistern in x hours. According to the question, $frac{1}{5}+frac{1}{6}-frac{1}{x}=frac{1}{10}$ $Rightarrow frac{6+5}{30}-frac{1}{x}=frac{1}{10}$ $Rightarrow frac{11}{30}-frac{1}{x}=frac{1}{10}$ $Rightarrow frac{1}{x}=frac{11}{30}-frac{1}{10}=frac{11-3}{30}=frac{8}{30}=frac{4}{15}$ $herefore x=frac{15}{4}$ hours. $herefore$ Capacity of the cistern $=left(frac{15}{4} imes 24 ight)$ gallons $=90$ gallons Alternative : Let A & B are inlets and C be the outlet.

Efficiency of C = (A + B + C) – (A + B)

= 3 – (6 + 5) = – 8 (–) sign shows that pipe C is

outlet.

Time taken by C to empty the tank

$=frac{30}{8} ext { hours }$

$herefore$ Capacity fo tank $=frac{30}{8} imes 24=90$ gallon