# Rates Practice - Word Problem

This aptitude practice question is a Work Time problem solving question. Concept tested: A word problem, where the crux of solving the question is framing a pair of equations and finding a solution.

## Question

**Concepts Covered**1. Framing equation for work time

2. Solving equations in 2 variables 2 concepts

Four men and three women can do a job in 6 days. When five men and six women work on the same job, the work gets completed in 4 days. How long will a woman take to do the job, if she works alone on it?

- 18 days
- 36 days
- 54 days
- None of these

** Correct Answer** Choice (3). A man and woman will take 54 days to complete the job.

## Explanatory Answer

Let the amount of work done by a man in a day be 'm' and the amount of work done by a woman in a day be 'w'.

Therefore, 4 men and 3 women will do 4m + 3w amount of work in a day.

If 4 men and 3 women complete the entire work in 6 days, they will complete \\frac {1} {6}^{th}) of the work in a day.

Hence, 4m + 3w = \\frac{1}{6}) ----- eqn (1)

From statement (2), we know 5 men and 6 women take 4 days to complete the job.

i.e., 5 men and 4 women working together will complete \\frac{1}{4})th of the job in a day.

So, 5m + 6w = \\frac{1}{4}) ----- eqn (2)

2 * eqn(1) - eqn (2):

8m + 6w - (5m + 6w) = 2 * \\frac{1}{6}) - \\frac{1}{4})

3m = = \\frac{1}{12}) or m = \\frac{1}{36}).

i.e., a man does \\frac {1}{36}^{th}) of the work in a day.

Substitute the value of m in eqn (1), we get 4 x \\frac{1}{36}) + 3w = \\frac{1}{6})

=> 3w = \\frac{1}{6}) - \\frac{1}{9}) = \\frac{3 - 2}{18}) = \\frac{1}{18})

Or w = \\frac{1}{54}).

i.e. a woman does \\frac {1}{54}^{th}) of the work in a day.

Hence, she will take 54 days to do the entire work.

The correct answer is Choice (3).

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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