Question : Pipes A and B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than A to fill the cistern, then what will be the respective time in which A and B will fill the cistern separately?
Option 1: 15 min and 10 min
Option 2: 15 min and 20 min
Option 3: 25 min and 20 min
Option 4: 10 min and 15 min
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Correct Answer: 10 min and 15 min
Solution : Let the time taken by A to fill the cistern be $x$ minutes. So, the time taken by B to fill the cistern is $x+5$ minutes. Time taken by A and B to fill the cistern = 6 minutes Part of cistern filled by A and B in a minute $= \frac{1}{6}$ Part of cistern filled by A in a minute $= \frac{1}{x}$ Part of cistern filled by B in a minute $=\frac{1}{x+5}$ Part of cistern filled by A and B together in a minute $= \frac{1}{x}+\frac{1}{x+5}$ ⇒$\frac{1}{x}+\frac{1}{x+5}=\frac{1}{6}$ ⇒ $12x+30=x^2+5x$ ⇒ $x^2-7x-30=0$ ⇒ $x=-3,10$ $\therefore x=10$ (–3 is neglected because time can't be negative) Time taken by B = 10 + 5 = 15 min Hence, the correct answer is '10 min and 15 min'.
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