Shortcuts to solve Time and Work Problems
Problems on ‘Time and Work’ are very common in competitive exams like Banking, SSC, CSAT, etc. Knowing the shortcut methods for solving such Quantitative Aptitude problems will give you an edge as most competitive exams also test your time management skills.
Time and Work Basic Formula
If a person completes a job in ‘n’ days then his 1 day’s work is given by:
And his efficiency is given by:
Relationship between Efficiency and Time
Efficiency and Time are inversely proportional , i.e., if X is 50% efficient as Y, then X takes twice the time taken by Y or if X is twice efficient as Y then X takes half the time taken by Y to finish the job.
Time and Efficiency in Ratio
If the ratio of efficiency of A and B is x: y, then the ratio of the time taken to finish the job by them is:
Relationship between Time, Constant Work and Efficiency
When the work done is considered in terms of fraction, then the whole work is represented as 1. When the work done is considered in terms of percentage, then the whole work is represented as 100%.
As mentioned before,
As 1 is a constant and considered fraction,
And when considered in percentage,
Some Shortcut formulas:
• If A does a work in ‘a’ hours and B in ‘b’ hours then they can together do the job in:
• If A takes ‘a’ hours more than the time taken by A and B together to do a job and if B takes ‘b’ hours more than the time taken by A and B together to do the same job, then they can together finish the job in:
• If A does a job in ‘a’ hours and A and B together take ‘x’ hours to finish a job then B alone will take:
• If A does a job in ‘a’ hours and B in ‘b’ hours and A, B and C together in ‘x’ hours to finish a job then:
I. C alone will take
II. A and C together will take
III. B and C together will take
Example: Priya can do a piece of work in 16 days while Riya can do the same work in 20 days. How long should it take both Priya and Riya to do the same work together?
Both Priya and Riya together can finish the work in