Time and Work Notes | Study Quantitative Techniques for CLAT - CLAT

CLAT: Time and Work Notes | Study Quantitative Techniques for CLAT - CLAT

The document Time and Work Notes | Study Quantitative Techniques for CLAT - CLAT is a part of the CLAT Course Quantitative Techniques for CLAT.
All you need of CLAT at this link: CLAT

Introduction 

Work is defined as something which has an effect or outcome; often the one desired or expected. The basic concept of Time and Work is similar to that across all Arithmetic topics, i.e. the concept of Proportionality.

Efficiency is inversely proportional to the Time taken when the amount of work done is constant.

To solve problems on ‘time and work’ the following simple facts should be remembered:

  • If a person can do work in 5 days, then in one day he will do 1/5th of the whole work. Conversely, if a man can do 1/5th of the work in one day, he will complete the whole work in 5 days.
  • If the number of men engaged to do a piece of work be increased in a certain ratio, the time required to do the same work will be decreased in the same ratio and vice versa. Thus if the number of men is changed in the ratio of 3:7, the time required will be changed in the ratio of 7:3.

Time and Work Notes | Study Quantitative Techniques for CLAT - CLAT

  • If A is twice as good a workman as B then A will take one-half of the time taken by B to do a certain piece of work.
  • To sum up if M1 persons working T1 hours a day can do W1 work in D1 days and M2 persons working H2 hours a day can do W2 work in D2 days, then the following equation will hold good.
    Time and Work Notes | Study Quantitative Techniques for CLAT - CLAT

Solved Examples

Example 1. A does work in 10 days and B does the same work in 15 days. How many days they will take to do the work together.

Sol. A does the work in 10 days, so A’s one-day work = 1/10

B does the work in 15 days, so B’s one day work = 1/15

Work done by A and B in one day = 1/10 + 1/15 = 5/30 = 1/6

Thus, A and B together will be able to finish the work in 6 days.

Try yourself: A can finish a work in 18 days and B can finish the same work in 9 days. If they work together, what part of the work will they be able to finish in a day. 
View Solution


Example 3. A tyre has two punctures. The first puncture alone can empty the tyre in 9 minutes and 2nd puncture alone can empty the tyre in 6 minutes. How long will both the punctures take to flat the tyre. 

Sol. The first puncture takes 9 minutes to flatten the tyre, so first puncture’s one-minute work = 1/ 9  

The second puncture takes 6 minutes to flatten that tyre, so second puncture’s one-minute work = 1/6

So work done by both punctures in one minute = 1/9 + 1/6 = 5/18

Thus, both punctures together will take 18/5 minutes to flatten the tyre.

Example 5. A and B together can finish a job in 15 days. If A alone can finish the job in 25 days, in how many days can B alone finish the job. 

Sol. A and B together can finish the job in 15 days, so their one day work = 1/15
A alone can finish the job in 25 days, so A’s one day work = 1/25

B’s one day work =  Time and Work Notes | Study Quantitative Techniques for CLAT - CLAT

Thus, B alone can finish the job in 75/2 days.

Example.6. A and B together can build a house in 25 days. They work together for 15 days and then B goes away. A finishes the rest of the work in 20 days. How long will each take to finish the job working separately?

Sol. A+B can finish the work in 25 days, so one day work = 1/25
They work together for 15 days, so the work done by A+B in 15 days = Time and Work Notes | Study Quantitative Techniques for CLAT - CLAT

Remaining job = Time and Work Notes | Study Quantitative Techniques for CLAT - CLAT  

To complete 2/5 of work in 20 days, A can complete one work in Time and Work Notes | Study Quantitative Techniques for CLAT - CLAT = 50 days 

B’s one day work = 1/25 – 1/50 = 1/50    

So B can finish the whole work in 50 days.

Try yourself:
A man can do a job in 5 days but with the help of his son he can do it is 3 days. In what time can the son do it alone. 
View Solution


Ex.7. A can finish a job in 10 days, B in 12 days and C in 10 days. In how many days will they finish the job if they work together. 

Sol. A’s one day work = 1/10

B’s one day work = 1/12

C’s one day work = 1/10

A+B+C’s one day work = 1/10 + 1/12 + 1/10 = (6+5+6)/60 = 17/60

Thus, together they can complete the work in 60/17 days.

Questions on Pipes and Cisterns

Example 9. Tap A can fill a tank in 8 hours. Outlet B can empty the tank in 12 hours. If both are kept open, how long will it take to fill the tank? 

Sol. Tap A can fill the tank in 8 hours, so Tap A’s one-hour work = 1/8

Tap B can empty the tank in 12 hours, so Tap B’s one hour work = 1/12

Tap A and Tap B’s one hour work = 1/8 – 1/12 = (3 – 2) / 24  = 1/24

Thus, the tank will be full after 24 hours.

Example 10. 8 Taps can fill a reservoir in 90 minutes. In how much time 12 taps can fill up the same reservoir if all the taps have equal capacity. 

Sol. 8 taps fill the reservoir in 90 minutes

One taps fill the reservoir in 90 x 8 minutes.

12 taps fill the reservoir in = (90 x 8) / 12 = 60 minutes.

Try yourself:Tap A and B can separately fill a tank in 10 hours and 15 hours respectively. If both the taps are opened together, how long will it take for the tank to be full?
View Solution


Example 11. Pipe A can fill a tank in 3 hours. Pipe B can fill it in 4 hours. An outlet pipe C can empty the filled-in tank in 6 hours. If all the three pipes are kept open simultaneously, in how many hours will the tank be half full? 

Sol. Pipe A can fill the tank in 3 hours, so Pipe A will fill in one hour =  1/3

Pipe B can fill the tank in 4 hours, so pipe B will fill in one hour = 1/4

Pipe C can empty the tank in 6 hours, so in one-hour pipe C will empty = 1/6

Pipe A + Pipe B + Pipe C = 1/3 + 1/4 - 1/6 = Time and Work Notes | Study Quantitative Techniques for CLAT - CLAT

So three pipes can fill the tank in 12/5 hours.

Thus, ½ tank will be filled in ½ x 12/5 = 6/5 hours.

Try yourself:Ex.13. Tap A fills a tank in 2 hours. Outlets B and C can empty the tank in 4 hours and 3 hours respectively. If the tank is empty and A and B are opened, how long will it take to fill the tank. After the tank is full A, B, C are all opened, in how many hours will the tank be empty. 
View Solution

The document Time and Work Notes | Study Quantitative Techniques for CLAT - CLAT is a part of the CLAT Course Quantitative Techniques for CLAT.
All you need of CLAT at this link: CLAT

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