PPT: Time & Work | CSAT Preparation - UPSC PDF Download

 Page 1


Time & Work
Page 2


Time & Work
Introduction to Time & 
Work
What is Work?
Something that produces an outcome or effect.
Why Important?
A critical topic in competitive exams due to its wide 
applications.
Core Idea: Efficiency ? 1/Time Taken
Less time = Higher efficiency.
E xa mp le: If A takes 5 days and B takes 10 days, A is 
twice as efficient.
Page 3


Time & Work
Introduction to Time & 
Work
What is Work?
Something that produces an outcome or effect.
Why Important?
A critical topic in competitive exams due to its wide 
applications.
Core Idea: Efficiency ? 1/Time Taken
Less time = Higher efficiency.
E xa mp le: If A takes 5 days and B takes 10 days, A is 
twice as efficient.
Work Done in One Day
Formula
If a person completes a work in n days, one 
day's work = 1 / n.
Also called ca p a city.
Work Done = Time T aken × Rate of Work
Example
If A finishes a job in 6 days:
One day's work = 1/6 of the job.
Page 4


Time & Work
Introduction to Time & 
Work
What is Work?
Something that produces an outcome or effect.
Why Important?
A critical topic in competitive exams due to its wide 
applications.
Core Idea: Efficiency ? 1/Time Taken
Less time = Higher efficiency.
E xa mp le: If A takes 5 days and B takes 10 days, A is 
twice as efficient.
Work Done in One Day
Formula
If a person completes a work in n days, one 
day's work = 1 / n.
Also called ca p a city.
Work Done = Time T aken × Rate of Work
Example
If A finishes a job in 6 days:
One day's work = 1/6 of the job.
Combined Work
Formula
If A takes a days and B takes b days:
Combined one day's work = 
1/a + 1/b = (a + b)/(ab).
Example
A takes 10 days, B takes 12 days:
Combined work per day = 1/10 + 1/12 = 
11/60.
Time together = 60/11 j 5.45 days.
Page 5


Time & Work
Introduction to Time & 
Work
What is Work?
Something that produces an outcome or effect.
Why Important?
A critical topic in competitive exams due to its wide 
applications.
Core Idea: Efficiency ? 1/Time Taken
Less time = Higher efficiency.
E xa mp le: If A takes 5 days and B takes 10 days, A is 
twice as efficient.
Work Done in One Day
Formula
If a person completes a work in n days, one 
day's work = 1 / n.
Also called ca p a city.
Work Done = Time T aken × Rate of Work
Example
If A finishes a job in 6 days:
One day's work = 1/6 of the job.
Combined Work
Formula
If A takes a days and B takes b days:
Combined one day's work = 
1/a + 1/b = (a + b)/(ab).
Example
A takes 10 days, B takes 12 days:
Combined work per day = 1/10 + 1/12 = 
11/60.
Time together = 60/11 j 5.45 days.
Previous Year Question
Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a 
job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days 
to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked 
alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number 
of days she would have taken to finish the job, cannot be? 
A: 17
B: 21
C: 16
D: 20
Solution: Let the work done by Rahul, Rakshita, and Gurmeet be a, b, and c units per day, 
respectively, and the total units of work are W.
Hence, we can say that 7(a+b+c) < W ( Rahul, Rakshita, and Gurmeet, working together, would have 
taken more than 7 days to finish a job).
Similarly, we can say that 15(a+c) > W ( Rahul and Gurmeet, working together would have taken 
less than 15 days to finish the job)
Now, comparing these two inequalities, we get: 7(a+b+c) < W < 15(a+c)
It is also known that they all worked together for 6 days, followed by Rakshita, who worked alone 
for 3 more days to finish the job. Therefore, the total units of work done is: W = 6(a+b+c)+3b
Hence, we can say that 7(a+b+c) < 6(a+b+c)+3b < 15(a+c)
Therefore, (a+b+c) < 3b => a+c < 2b, and 9b < 9(a+c) => b < a+c
=> a+b+c < 3b => 7(a+b+c) < 21b , and 15b < 15(a+c)
Hence, The number of days required for b must be in between 15 and 21 (both exclusive).