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CAT 2017 Slot 2 — QA Question 8

Pipes & CisternsEasy

A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours. If the outlet pipe is open then the inlet pipe fills the empty tank in 10 hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full?

Answer & solution

Correct answer: 20

  • 20

  • B

    30

  • C

    40

  • D

    45

Solution

Easy

Work in "tank per hour" rates. The inlet rate is known; with both pipes open the net fill rate is known, so subtract to get the outlet rate, then find its emptying time.

1

Known rates. Inlet fills in 88 h; inlet minus outlet fills in 1010 h. Let the outlet empty the tank in xx h.

inlet=18,net=110\begin{aligned} &\text{inlet}=\frac18,\qquad \text{net}=\frac{1}{10} \end{aligned}
2

Solve for the outlet rate. Net == inlet −- outlet.

18−1x=110⇒ 1x=18−110=5−440=140⇒ x=40(outlet empties full tank in 40 h)\begin{aligned} &\frac18-\frac1x=\frac{1}{10}\\ &\Rightarrow\ \frac1x=\frac18-\frac{1}{10}=\frac{5-4}{40}=\frac{1}{40}\\ &\Rightarrow\ x=40 \quad\text{(outlet empties full tank in 40 h)} \end{aligned}
3

Half the tank. At a uniform rate, emptying half takes half the time.

402=20 hours\begin{aligned} &\frac{40}{2}=20\ \text{hours} \end{aligned}
Time to go full→half=20 hours\text{Time to go full}\to\text{half}=20\ \text{hours}

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CAT 2017 Slot 2 QA Q8: A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty — Solution | TheCATExam