Expert Advises to Solve Time and Work Problems in 3 ways
In every competitive exam, Time and Work topic is must. Applicants who are going to appear for the competitive and private exams, those can prepare Time and Work problems also. Large numbers of candidates can feel very tough to prepare Time and Work problems. Here we are provide the expert advises to solve the Time and Work Problems easily with the below steps with examples at our website. Candidates can download and practice the Time and Work problems with these simple formulas.
3 Ways to Solve Time and Work Problems:
Step 1: Calculate Time to Complete Work by 2 or more people:
In this step, you have to calculate time taken by 2 or more people to do a job. In the question, you will be given the time required by each member individually. You have to calculate the required time if they Time and Work together.
Rahul takes 5 hours to do a job. Benny takes 8 hours to do same job. How long should it take for Rahul and Benny, working together but independently, to do the same job?
From the question, you can write down the below values,
Part of work done by Rahul in one hour = 1/5……..Value 1
Part of work down by Benny in one hour = 1/8……value 2
Part of work done by Rahul and Benny Together = Value 1 + Value 2 = 1/5+1/8 = 13/40
Now, you can calculate total hours required by both to complete the work using direct proportion table.
Number of Hours required by both to complete the work together = 1*1/(13/40) = 40/13 = 3 1/13 Hours.
Step 2: Extension to Step 1 when days and Hours are given in Time and Work Problem:
In this step, you will see time as a measure of days and working hours per day. Below example will help you to understand better.
Arjun can do a piece of work in 5 days of 8 hours each and china can do it in 4 days or 6 hours each. How long will they take to do it working together 7 ½ hours a day?
In question, you can see that Arjun can complete the work in 5 days working 8 hours per day.
Therefore, Arjun can complete the work in (5 days x 8 hours/day) = 40 hours
Similarly, Chinna can complete the work in (4 days x 6 hours/day) = 24 hours
Now, you have to proceed like type 1.
Part of work that Arjun can do in 1 hour = 1/40 … value 1
Part of work that Chinna can do in 1 hour = 1/24 … value 2
Part of work that Arjun and Chinna can do together in 1 hour = value 1 + value 2
= 1/40 + 1/24 = (3+5)/120 = 8/120
You can calculate total hours required by both to complete the work using direct proportion table
|?||1 (1 represents full work)|
Both will finish the work in 1 x 1 / (8/120) = 120/8 hours.
You have to calculate number of days required if they work 7 ½
or 15/2 hours each day. Now, you can calculate the number of days required using direct proportion table method.
Therefore, if the friends work 15/2 hours each day, the total number of days to complete the work
= 120/8 x 2/15 = 2 days
Type III: Equations Based Time and Work Problems
A and B can built a wall in 12 days, B and C can do it in 16 days and A and C can do it in 18 days. In how many days will A, B and C finishes it separately?
You have to assume the following.
Let As 1 day of work be X,
Bs 1 day of work be Y,
and Cs 1 day of work be Z.
Part 1: Form Equations Based on Question Data
From the question you know that A and B can build the wall in 12 days.
Part of work completed by A and B together in 1 day = 1/12
Or A’s 1 day of work + B’s 1 day of work = 1/12
Or X + Y = 1/12 … equation 1
You know that B and C can build the wall in 16 days
Part of work completed by B and C together in 1 day = 1/16
Or Bs 1 day of work + Cs 1 day of work = 1/16
Or Y + Z = 1/16 … equation 2
You also know that A and C can build the wall in 18 days
Part of work completed by A and C together in 1 day = 1/18
Or As 1 day of work + Cs 1 day of work = 1/18
Or X + Z = 1/18 … equation 3
Part 2: Let Us Solve The Equations
If you add equations 1,2 and 3, you will get the following.
2 (X + Y + Z) = 1/12 + 1/16 + 1/18
2 (X + Y + Z) = (12 + 9 + 8)/144 = 29/144
Or, X + Y + Z = 29/288 … equation 4
- a) Subtract equation 1 from equation 4:
(X + Y + Z) – (X + Y) = 29/288 – 1/12
Or, Z = 29-24 / 288
Or, Z = 5/288
- b) Subtract equation 2 from equation 4:
(X + Y + Z) – (Y + Z) = 29/288 – 1/16
Or, X = 29-18 / 288
Or, X = 11/288
- c) Subtract equation 3 from equation 4:
(X + Y + Z) – (X + Z) = 29/288 – 1/18
Or, Y = 29-16 /288
Or, Y = 13/288
A’s 1 day of work = X = 11/288
Therefore, A can complete the work in 288/11 = 26 2/11 days
B’s 1 day of work = Y = 13/288
Therefore, B can complete the work in 288/13 = 22 2/13 days
C’s 1 day of work = Z = 5/288
Therefore, C can complete the work in 288/5 = 57 3/5 days