Question : Pipes A and B together can fill a tank in 10 hours. Pipes B and C together can fill the same tank in 12 hours. Pipes A and C together can fill the same tank in 15 hours. In how many hours can pipe B alone fill the same tank?
Option 1: $\frac{120}{7}$ hours
Option 2: $15$ hours
Option 3: $\frac{120}{11}$ hours
Option 4: $\frac{155}{13}$ hours
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Correct Answer: $\frac{120}{7}$ hours
Solution : Pipes A and B together can fill a tank in 10 hours. Pipes B and C together can fill the same tank in 12 hours. Pipes A and C together can fill the same tank in 15 hours. According to the question, Work done by (A + B) = $\frac{1}{10}$ .................(1) Work done by (B + C) = $\frac{1}{12}$.................(2) Work done by (C + A) = $\frac{1}{15}$ ..................(3) Adding all the equations we get, 2(A + B + C) = $\frac{1}{10}$ + $\frac{1}{12}$ + $\frac{1}{15}$ ⇒ A + B + C = $\frac{1}{2}(\frac{15}{60})$ = $\frac{1}{8}$ So, A, B and C together in 1 hour can do $\frac{1}{8}$ part A and C in 1 hour can do $\frac{1}{15}$ part So, B alone in 1 hour can do ($\frac{1}{8}-\frac{1}{15}$) = $\frac{7}{120}$ Therefore, the time required by B to fill the tank = (1 ÷ $\frac{7}{120}$) = $\frac{120}{7}$ hours Hence, the correct answer is $\frac{120}{7}$ hours.
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