# Solve Time and Work Questions

Time and Work Questions are an important topic to be covered in competitive exam preparation be it for IBPS Clerk, PO, RRB, SO, or SBI Clerk or PO. The number of questions and the complexity of questions vary from exam to exam every year.

Time and Work Questions are complex in nature and require an understanding of Percentage Calculation, Ratio and ProportionAverage, and Math Tables. Solved examples on Time and Work Questions and Practice on Time and Work Questions are given in this article.

Nowadays, questions in exams are mixed with multiple concepts and it requires practice and a deep understanding of basic concepts along with quickly identifying numbers.

## Concept of Time and Work Questions

To complete any piece of work or the complete task requires time and effort from skilled or unskilled workers. Relation between work and time is considered in the planning of work and accordingly work is started.

In a real-world scenario, Time and Work Questions are very essential concepts to evaluate the progress of work and also to measure the scheduled completion of Work. Also, the number of workers required to complete any work is to be considered and plays and very helpful in reducing completion time.

Let’s understand work and time questions with the below example:

Example: A building has to be built and for this work given time of completion was 30 days. If one worker can complete this task in 30 days then we can say that 1/30th part of the work is completed in one day.

## Time and Work Questions in Ratio

Time and Work Questions in Ratio for two-person can be said as inversely proportional to each other. In Other Words, we can say that if the work efficiency of both persons is different then the time taken for work to complete is inversely proportional.

For Example: If X takes 4 days to complete work and Y is 4 times faster than X then find the time taken by Y?
Solution: The work Ratio between X and Y is 1:4
The time Ratio between X and Y will be inverse, as 4:1.
Hence, the time taken by Y to complete work will be 1 Day.

## Combine Time and Work Formula

1. If ‘A’ and ‘B’ can finish the work in ‘X’ and ‘Y’ days respectively, then A’s one day’s work will be 1/X and B’s one day’s work will be 1/Y. Now A and B’s one day’s work will be
=> 1/X + 1/Y = (X +Y)/ X x Y
So together A and B can complete work in
=> X x Y / (X + Y)
1. If ‘A’, ‘B’, and ‘C’ can finish the work in ‘X’, ‘Y’, and ‘Z’ days respectively, then A’s one day’s work will be 1/X, B’s one day’s work will be 1/Y and C’s one day’s work will be 1/Z. Now A, B and C’s one day’s work will be => 1/X + 1/Y + 1/Z = (XY +YZ + XZ)/ X x Y x Z
So together A, B, and C can complete work in
=> X x Y x Z/ (XY + YZ + XZ)
1. If ‘A’ and ‘A and B’ can finish the work in ‘X’ and ‘Y’ days respectively, then A’s one day’s work will be 1/X and A and B’s one day’s work will be 1/Y. Now B’s, one day’s work will be
=> 1/Y – 1/X = (X – Y) / X x Y
So B can complete work in
=> X x Y / (X – Y)
1. If ‘A’ and ‘B’ can finish the work in ‘X’ days, If ‘B’ and ‘C’ can finish the work in ‘Y’ days and If ‘A’ and ‘C’ can finish the work in ‘Z’ days respectively, then A and B’s one day’s work will be 1/X, B and C’s one day’s work will be 1/Y and C and A’s one day’s work will be 1/Z. Now A, B and C’s one day’s work will be
=> 1/X + 1/Y + 1/Z = 2(A +B + C)
So together A, B, and C’s one day’s work will be:
=> A + B + C = (1/X + 1/Y + 1/Z)/2
So together A, B, and C can complete work in
=> A + B + C = 2 / (1/X + 1/Y + 1/Z)
=> A + B + C = 2(X x Y x Z)/ (XY + YZ + XZ)

## Solved Examples on Time and Work Questions

Below are the solved examples on Time and Work Questions:

Example 1: If A takes 16 days to complete work and B is 4 times faster than A. Find how much time B will take to complete the work?

Solution 1: As per the ratio we are able to understand that the Work Ratio between A and B is 1 : 4. Then Time ratio will be inversely proportional to the Work ratio, so the Time ratio between A and B is 4 : 1.
If A takes 16 Days then the time ratio is 4.
Then B will take 16 / 4 = 4 Days to complete the work.

Example 2: If A takes 40 days to complete work and B is 25% faster than A. Find how much time B will take to complete the work?

Solution 2: As per the ratio we are able to understand that the Work Ratio between A and B is 4 : 5. Then Time ratio will be inversely proportional to the Work ratio, so the Time ratio between A and B is 5 : 4.
If A takes 40 Days then the time ratio is 5.
Then B will take 4 x (40 / 5) = 32 Days to complete the work.

Example 3: If A takes 3 days to complete work, and B takes 6 days to complete work then both together will complete work in how much time?

Solution 3: As per the above formula of combined work
One day’s work by A is 1/3.
One day’s work by B is 1/6.
One day’s work by A and B will be
=> 1/3 + 1/6 = (6 + 3) / (6 x 3) = 9 / 18 = 1 / 2
Hence, together A and B will complete the work in 2 Days.

Example 4: If A takes 10 days, B takes 15 days and C takes 12 days to complete work respectively. Then together how many days A, B, and C will complete work?

Solution 4: As per the above formula of combined work
One day’s work by A is 1/10.
One day’s work by B is 1/15.
One day’s work by C is 1/12.
One day’s work by A, B, and C will be
=> 1/10 + 1/15 + 1/12 {Note: Finding LCM of 10, 15 and 12}
=> (6 + 4 + 5) / 60 = 15 / 60 = 1/4
Hence, together with A, B, and C will complete the work in 4 Days.

Example 5: If A takes 10 days and B takes 15 days to complete work, respectively. Then if A and B start working together but after 5 days A leave and B alone finish work. Find how many days total work was completed?

Solution 5: As per the above formula of combined work
One day’s work by A is 1/10.
One day’s work by B is 1/15.
One day’s work by A and B will be
=> 1/10 + 1/15 = (10 + 15) / (10 x 15) = 25 / 150 = 1 / 6
Hence, together A and B will complete work in 6 Days. But A left after 5 days. Total work completed in 5 days was 5/6 and now remaining was 1/6 work that B will do alone.
=> 15 x 1 /6 = 2.5 Days
Total days have taken to complete work = 5 + 2.5 = 7.5 days.

## Practice Time and Work Questions

Below are the practice Time and Work Questions:

1. If A takes 60 days to complete work and B is 50% more efficient than A. Find in how many days B will complete work?
2. If B takes 50 days to complete work and A is 25% less efficient than B. Find in how many days A will complete work?
3. If A takes 10 days and B takes 8 days then together they’ll complete work in how many days?
4. If A takes 15 days and B takes 20 days then together they’ll complete work in how many days?
5. If A takes 18 days, B takes 20 days and C takes 15 days then together they’ll complete work in how many days?
6. If A takes 60 days, B takes 50 days and C takes 75 days then together they’ll complete work in how many days?
7. If A and B take 60 days, B and C takes 50 days, and C and A take 75 days, respectively to complete work. Then together they’ll complete work in how many days?
8. If A and B take 20 days, B and C takes 18 days, and C and A takes 15 days, respectively to complete work. Then together they’ll complete work in how many days?
9. If A takes 60 days, B takes 50 days and C takes 75 days to complete work respectively. If after 10 days of working together A leaves then in how many days B and C will complete the remaining work?
10. If A takes 60 days, B takes 50 days and C takes 75 days to complete work respectively. If after 10 days of working together A leaves, and after A left, C also left after 10 more days. Then in how many days B will complete the remaining work?

## Final Words

Practicing the above Time and Work questions is not the end of your practice, but it’s a start of a new journey to apply logic to Time and Work questions and solutions with multiple approaches in a right and faster way.

For cracking competitive exams one must practice Time and Work questions without a calculator is a must. At last, during the exam, if a solution for Time and Work questions cannot be found easily then mark that question to revisit and move ahead instead of wasting time and energy.