# Rates Word Problem : Pipes cisterns

This aptitude practice question is a Pipes Cisterns problem solving question. Concept tested: How to frame equations for word problem in pipes and cistern accounting for some pipes filling and others emptying a tank.

## Question

**Concepts Covered**1. How to frame equations for pipes cistern word problems?

2. Solving simple equations 2 concepts

Pipe A usually fills a tank in 2 hours. On account of a leak at the bottom of the tank, it takes pipe A 30 more minutes to fill the tank. How long will the leak take to empty a full tank if pipe A is shut?

- 2 hours 30 minutes
- 5 hours
- 4 hours
- 10 hours

** Correct Answer** Choice (4). The leak at the bottom of the tank will empty the tank in 10 hours.

## Explanatory Answer

Pipe A fills the tank normally in 2 hours.

Therefore, it will fill \\frac{1}{2}) of the tank in an hour.

Let the leak take x hours to empty a full tank when pipe A is shut.

Therefore, the leak will empty \\frac{1}{x}) of the tank in an hour.

The net amount of water that gets filled in the tank in an hour when pipe A is open and when there is a leak =

\\frac{1}{2}) - \\frac{1}{x}) of the tank. ----- (1)

When there is a leak, the problem states that it takes two and a half hours to fill the tank. i.e. \\frac{5}{2})hours.

Therefore, in an hour, \\frac{2} {5}^{th}) of the tank gets filled. ----- (2)

Equating (1) and (2), we get \\frac{1}{2}) - \\frac{1}{x}) = \\frac{2}{5})

=> \\frac{1}{x}) = \\frac{1}{2}) - \\frac{2}{5}) = \\frac{1}{10})

=> x = 10 hours.

The problem can also be solved without putting pen to paper as follows.

Pipe A takes 2 hours to fill the tank. Therefore, it fills half the tank in an hour or 50% of the tank in an hour.

When there is a leak it takes 2 hours 30 minutes for the tank to fill. i.e \\frac{5}{2})hours to fill the tank or \\frac {2}{5}^{th}) or 40% of the tank gets filled.

On account of the leak, (50 - 40)% = 10% of the water gets wasted every hour.

Therefore, the leak will take 10 hours to drain a full tank.

The correct answer is Choice (4).

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## XAT TANCET Practice Questions - Listed Topic wise

- Number Theory
- Permutation Combination
- Probability
- Inequalities
- Geometry
- Coordinate Geometry
- Mensuration
- Trigonometry
- Data Sufficiency
- Percentages
- Profit Loss
- Ratio Proportion
- Mixtures & Alligation
- Speed Distance & Time
- Pipes, Cisterns & Work, Time
- Simple & Compound Interest
- Races
- Averages & Statistics
- Progressions : AP, GP & HP
- Set Theory
- Clocks Calendars
- Linear & Quadratic Equations
- Functions
- English Grammar
- General Awareness