**Free Online Preparation for CAT 2009 with Minglebox e-CAT Prep. Cover basic concepts of Time and Work under Quantitative Aptitude for MBA Entrance Exam Preparation with Study material, solved examples and tests prepared by CAT coaching experts. **

If a person A can do a piece of work in 'a' days, then working at the same uniform speed A will do fraction of the work in one day.

For example,

Days taken to complete 'a' work |
25 |
12.5 |
1/2 |

Fraction of work done in a day |
1/25 th |
1/12.5 th |
2 |

Working together – If working alone can do some work in 'a' days and if another person B working alone can do it in 'b' days , then if A and B

start working together the amount of work done by A & B in one day =

Therefore total work is done by A and B working together in days

Note: Remember it is work done that is additive and not number of days.

If A completes a work in 'a' days working alone and B completes it in 'b' days working alone, then intended of assuming the work as 1 unit we can assume total work to be LCM of (a,b) this will avoid the fraction in the calculation.

Proportionality (concept of efficiency )

If A is thrice as efficient as B then if A takes 12 days to complete a work then B will take = 36 days to complete the work . Whenever

relative efficiency of team member is given the most suitable approach is to consider the capacities of each team member in terms of any given

team member.

Amount of Work done is directly proportional number of person employed to do the work and days worked.

If amount of work is constant then number of days taken to complete the work is inversely proportional to days taken.

Men , Women and children working in a given project.

Question

If work can be done in 10 days by 4 men or 6 women or 10 children. How many days are required for 3 men , 8 women and 6 days to complete it?

Solution

1 Man will take 40 days , hence 3 men will take 40/3 days to complete it

1 women will take 60 days, hence 8 women will take 60/8 days

1 child will take 100 days , hence 6 days will take 100/6 days

then total time taken if they all worked together is = days.

Question

A house can be built by A in 50 days and B can demolish it in 60 days . If A and B work on alternative days , in how many days will the house be built , assuming A stars first and once house is built completely B days not demolish it?

Solution

In 2 days cycle amount of work done = but does that mean work gets done in 600 days . Think again as a finisher th of

the work in one days , hence if work done is less then then A finisher the work and B does not demolish it .

In two days amount of work done is th therefore th fraction of the work is finished in

588 days work left to be done on days is which A will finish. Hence work gets finished in 589 days.

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