Time and Work
Aptitude Questions and Answers



1. What is Work?

Technically speaking, Work is the quantity of energy transferred from one system to another but for question based on this topic, Work is defined as the amount of job assigned or the amount of job actually done.

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2. Analogy with Time-Speed-Distance

Problem on work are based on the application of concept of ratio of time and speed. Work is always considered as a whole or one. There exists an analogy between the time-speed-distance problems and work.

Work based problem are more or less related to time speed and distance.

Above mentioned definition of work throws light on three important points.

Work = 1 (It is always measured as a whole) = Distance

Rate at which work is done = speed

Number of days required to do the work = Time

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Example:

If Ram and Raman can do a job in 10 days and 15 days independently, how many days would they take to complete the same job working simultaneously?

Solution:

If total work is $W$, Ram's rate of working = $\dfrac{W}{10}$ per day and that of Raman = $\dfrac{W}{15}$ per day.

Thus when working simultaneously, rate of work done = $\dfrac{W}{10} + \dfrac{W}{15}$ and thus time taken:

$=\dfrac{W}{W/10 + W/15} = \dfrac{15*10}{15+10}$

$= 6 \text{ Days}$

Alternatively:

above problem can be worked out assuming work to be just 1 unit and thus eliminating use of W.

Assume the total work to be the LCM of the days taken individually i.e. LCM of 10 & 15 i.e. 3o units of work.

Thus Ram’s rate of working = 3 units per day and Raman’s rate of working = 2 units per day.

When working simultaneously, $3+2=5$ units of work is done every day and thus it would take $30/5 = 6$ Days.

Note:

ALL problems or work can be solved in either way and both ways take almost the same time as there are exactly the same numbers of calculations involved. However if you are not comfortable with fraction, the approach using LCM may seem better to you.

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3. Important Formulae

3.1. Work from Days

If A can do a piece of work in n days, then A's 1 day's work $ = \dfrac{1}{n}$

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3.2. Days from Work

If A's 1 day's work $=\dfrac{1}{n}$, then A can finish the work in n days.

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3.3. Ratio

1. If A is thrice as good a workman as B, then:

2. Ratio of work done by A and B $= 3 : 1.$

3. Ratio of times taken by A and B to finish a work $= 1 : 3$

4. If A is $x$ times as good a workman as B, then he will take $\left(\dfrac{1}{x}\right)^{th}$ of the time by B to do the same work.

5. A and B can do a piece of work in 'a' days and 'b' days respectively, then working together, they will take $\dfrac{xy}{x+y}$ days to finish the work and in one day, they will finish $\left(\dfrac{x+y}{xy}\right)^{th}$ part of work.

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