In this, we won’t discuss the basics and formulas of Time and Work, instead, we will be focusing on the tricks that are usually used to do these types of questions. In Quantitative Aptitude Tests, Time and Work problems are commonly asked questions and might seem complex if you’re not aware of its tricks to solve.
Like flip side of coin, there is also a completely different topic in time and work which is efficiency. In this, we will be discussing the efficiency problems of work and time.
Efficiency: Capability of an individual to do work.
Note: More efficient worker will finish work faster than less efficient worker
These types of questions mainly consist words such as work, efficiency, days and time.
Types of Questions Asked From Time and Work Problems
Together complete a work
- First find LCM of days that are required by all people to complete the work, to figure out total work
- After getting total work, calculate how much work is done by an individual in a day
- After finding each individual work per day, add them together to get total work done by them in a single day
- Divide the total work per day with actual work to get the day
- The quotient is your days
Q. A does a work in 3 days and B does the same work in 6 days. If both do the same work together in how many days it will get finished?
- LCM of A and B’s days to finish the same work = 3,6 = 6 work
- Calculating Work per day for each individual
- A does = 6/3 = 2 work per day
- B does = 6/6 = 1 work per day
- They together do the same work in a day = A + B =2+1 =3 work per day
- Now, find total work would be done in days = 6/3 = 2 days
They would require 2 days to finish the same work
When someone left his work
- Get the LCM to find total work
- Get each individual share of work done in a day
- Add up each individual’s per day to get total work per day
- Now, get the total days that is required to finish the total work
- Divide the total work by the given number of days in which they worked together
- From this you would get how much work has been done
- subtract it from total work to get remaining work
- Now, divide the remaining work by person’s work per day who didn’t leave his job
- You will get the days
Q. A does a work in 10 days and B does the same work in 20 days. They work together for 3 days after which B left the job. In many days the remaining work will get finished?
- LCM of A and B, Total Work = 20 unit
- A does = 20/10 = 2 unit per day, B does = 20/20 = 1 unit per day
- They work together per day = 2+1 = 3 unit per day
- They together can finish the work = 20/3 days
- B lefts, Till then the work done was = 3*3 = 9 unit
- Remaining work = 20-9 = 11 unit
A requires to finish remaining work = 11/2 day
Individual Work
- Find LCM of all the days to finish the work required by individual and when they work together, to get total work
- Calculate work per day by dividing total work by days
- Subtract per day work of individual from work together
Q. A and B together do a work in 10 days and A alone needs 15 days to finish the same work. Find how much days B would require to finish the same work?
- LCM of A and A+B = 15,10 = 30
- A does =3p/15 = 2 unit work per day. A+B = 30/10 =3 unit work per day
- B does = 3-2 =1 unit per day
- B requires= 30/1 = 3o days to finish the work
Types of Questions Asked From Time and Work Efficiency Problems
When efficiency is given in % and an individual’s days are given to complete a job and need to find days when they together work. i.e When A is _% more efficient than B
- Assume base work per day as 100 and likewise add or subtract %efficiency to 100
- Multiply %efficency with number of days to complete a job by an individual to get total work
- Add Assumed base work per day
- Divide total work by their total work per day to get days
Q. A is 30% more efficient than B. How much time will they take to complete a job by working together, which A alone could have done in 23 days?
Step 1. Assumed base work per day of B = 100, A’s work per day = 130
Step 2. Total Work = A’s efficiency * Days to require to finish a work, 130 * 23 = 2,990
Step 3. Together they finish a work = 100 + 130 = 230
Step 4: Total days = 2990/230 = 13 days
When efficiency is given in times and also given their together days to finish a work are given, we need to calculate to work done by individual
- Put their efficiency in the ratio
- To calculate one’s work = together days to finish work * (Sum of ratio / A or B’s ratio)
Q. A is twice efficient than B to finish a work. They together complete the same work in 20 days, then how many days A can alone finish the work?
Step 1. Ratio of their efficiency = A : B = 2:1
Step 2 A requires = 20 * (3/2)
30 Days
When efficiency is given in times and also given the difference of their days to complete the work. You require to find total work
- Put their efficiency in the ratio
- Assume a number in such a way that multiplying it on both the ratios would give their difference same as given in the question
- Now these new ratios are the days that they require to finish the work
- Find LCM it will give you total work
Q. A is twice as good as workman as B and therefore able to finish a work in 18 days less than B. What is total unit work?
Step 1. Ratio of their efficiency = A : B = 2:1
Step 2. 18 is the number, multiplying it with ratio will give the same difference as days difference given in the question
36 – 18 = 18 days
Step 3. A requires = 36 days
B requires = 18 days
Step 4. LCM of these is 36 which is nothing but total unit work
