HOW TO SOLVE TIME AND WORK PROBLEMS EASILY

About the topic "How to Solve Time and Work Problems Easily"

"How to Solve Time and Work Problems Easily" is a big question having had by the people who get prepared for competitive exams and study quantitative aptitude. Solving time and work problems is  never being easy and always it is a challenging one for any student. 

How to Solve Time and Work Problems Easily?

The answer  for the question "How to Solve Time and Work Problems Easily?" is purely depending upon the question that we have in the topic "Time and Work Problems". The techniques and methods we apply to solve problems in time and work  will vary from problem to problem.

The techniques and methods we apply to solve a particular  problem  will not work for another word problem in time and work.

Even though we have different techniques to solve word problems in different topics of math, let us see the steps which are most commonly involved in "How to Solve Time and Work Problems Easily"

Points to remember

1. If a person can do a piece of work in ‘m’ days, he can do (1/m) part of the work in 1 day.
2. If the number of persons engaged to do a piece of work be increased (or decreased) in a certain ratio the time required to do the same work will be decreased (or increased) in the same ratio.
3. If X is twice as good a workman as Y, then X will take half the time taken by Y to do a certain piece of work.
4. Time and work are always in direct proportion.
5. If two taps or pipes P and Q take ‘m’ and ‘n’ hours respectively to fill a cistern or tank, then the two pipes together fill (1/m)+(1/n) part of the tank in one hour. Entire tank is filled in mn/(m+n) hours.

Methods involved in solving time and work problems

Do you want to know "How to solve time and work problems easily"?  Just come to know the two methods which are applied to solve time and work problems easily.

1. " Part of the Work " method

2.  "L.C.M" method

To get answer for the question "How to Solve Time and Work Problems Easily? ", we have to be knowing the above two mentioned methods clearly.

Let us look at an example to clearly understand the method "Part of the work".

Problem:

A and B can complete a work in 12 days.B and C can complete the same work in 18 days. C and A can complete in 24 days. How many days will take for A, B and C combined together to complete the same amount of work?

Solution:

Step 1 :

Let us understand the given information. There are three information given in the question. 

1. A & B can complete the work in 12 days.

2. B & C can complete the work in 18 days.

3. A and C can complete the work in 24 days.

Step 2 :

Target of the question: No. of days taken by A, B & C together to complete the same work.

Step 3 :

From the basic concepts given above, we have the following.

(A+B) can complete(1/12) part of the work in 1 day

                                 A + B = 1/12 -----(1)

(B+C) can complete (1/18) part of the work in 1 day

                                B + C = 1/18 -----(2)

(A+C) can complete (1/24) part of the work in 1 day

                                 A + C = 1/24 -----(3)

Step 4 :

          (A+B) + (B+C) + (A+C) = 1/12 + 1/18 + 1/24                           

                       2A + 2B + 2C = (6+4+3)/72

                              2(A+B+C) = 13/72

                                  A+B+C = 13/144

     (A+B+C) can complete 13/144 part of the work in 1 day

Step 5 :

Therefore (A+B+C) can together complete the work in 144/13 days

                                        That is 11(1/3) days

Now, Let us look at an example to clearly understand "L.C.M method".

Problem:

A & B can do a work in 15 days, B & C in 30 days and A & C in 18 days. They work together for 9 days and then A left. In how many more days, can B and C finish the remaining work?

Solution:

Step 1 :

Let us understand the given information. There are three information given in the question. 

1. A & B can do the work in 15 days.

2. B & C can do the same work in 30 days.

3. A & C can do the same work in 18 days.

Step 2 :

Target of the question: A,B & C work together for 9 days and then A left. In how many more days, can B and C finish the remaining work?

Step 3 :

Let us find the L.C.M for the given number of days.

That is L.C.M of (15, 30, 18)  =  90

(L.C.M of the given number of days to be considered as total work)

So, Total work  =  90 units.

Step 4 :

          (A+B) can complete 6 units/day     (90/15 = 6)

          (B+C) can complete 3 units/day     (90/30 = 3)

          (A+C) can complete  5 units/day     (90/18 = 5)

Step 5 :

Adding the above three statements, we get,

                   (A+B) + (B+C) + (A+C)  =  14 units/day 

                                 2A + 2B + 2C = 14 units/day

                                    2(A + B + C) = 14 units/day

                                        A + B + C = 7 units/day

That is,  (A +B +C) together can complete 7 units of total work in one day.

Step 6 :

Work done by (A+B+C) in 9 days = 9x7 = 63 units.

So, (A+B+C) together completed 63 units of total work in 9 days.

Balance work to be completed = 90 - 63 = 27 units.

Step 7 :

This 27 units of work to be completed by (B+C). Because A left after 9 days of work.

(B+C) together can complete 3 units in one day.

No. of days taken by (B+C) to complete the work = 27/3 = 9 days

Hence, B & C finish the remaining work in 9 days.

We hope, you would have received answer for the question "How to solve time and work problems easily?" after having seen the steps involved in solving the above two problems in time and work .

Please click the below links to know "How to solve word problems in each of the given topics"

1. Solving Word Problems on Simple Equations

2. Solving Word Problems on Simultaneous Equations

3. Solving Word Problems on Quadratic Equations

4. Solving Word Problems on Permutations and Combinations

5. Solving Word Problems on HCF and LCM

6. Solving Word Problems on Numbers

7. Solving Word Problems on Time and Work

8. Solving Word Problems on Trains

9. Solving Word Problems on Time and Work.

10. Solving Word Problems on Ages.

11.Solving Word Problems on Ratio and Proportion

12.Solving Word Problems on Allegation and Mixtures.

13. Solving Word Problems on Percentage

14. Solving Word Problems on Profit and Loss

15. Solving Word Problems Partnership

16. Solving Word Problems on Simple Interest

17. Solving Word Problems on Compound Interest

18. Solving Word Problems on Calendar

19. Solving Word Problems on Clock

20. Solving Word Problems on Pipes and Cisterns

21. Solving Word Problems on Modular Arithmetic

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