Time and Work problems are the very frequently asked in the general aptitude section of GATE. These problems can be solved easily by applying shortcuts and tricks which make them highly scoring from GATE exam perspective.
This article will highlight the shortcuts and tricks for solving problems based on time and work.
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Shortcuts for Solving problems based on Time and Work
If X can do a piece of work in n days, then X’s one day’s work = 1/n
If X’s one day’s work = 1/n, then X can complete the work in n days
If X is thrice as good a workman than Y, then Ratio of work done by X and Y= 3:1.Ratio of time taken by X and Y to complete the work = 1:3
More Men Can Do More Work ;Less Men Can Do Less Work ;More men can work in Less Time ,Less Men can work in More Time
M1 D1W2 = M2D2W1 where M1 men can do W1 work in D1 days and M2 men can do W2 work in D .
M1 D1 h1W2 = M2D2h2W1 where M1 men can do W1 work in D1 days for h1 hours and M2 men can do W2 work in D2 days for h2
Level : Easy
Question: X can complete a piece of work in 18 days while Y takes 15 days to complete the same work. Y worked for 10 days and left the job. How many days would X alone take to complete the remaining work?
Solution: Y’s 10 day’s work = (1/15) * 10 = 2/3
Remaining work = (1- 2/3) = 1/3
Now, 1/18 work is done by X in 1 day
Therefore, 1/3 work is done by X in = 18 *(1/3) = 6 days
Level : Medium
Question : P and Q can complete a piece of work in 20 days and 12 days respectively. P started the work alone and after 4 days, Q joined him till the end of the work. How long did the work last?
Solution : Work done by P in 4 days = (1/20) * 4 = 1/5
Remaining Work = (1- 1/5) = 4/5
(P+ Q)’s 1 day’s work = (1/20 + 1/12) = 2/15
2/15 work is done by P and Q in 1 day.
So, 4/5 work will be done by P and Q in = (4/5 * 15/2) = 6 days
Therefore, total time taken = (6+4) days = 10 days.
Level : Difficult
Question: X can do a certain work in same time in which Y and Z could together do it. If X and Y could together do the work in 10 days and Z alone in 50 days, how many days would Y take to complete the work alone ?
Solution: (X + y)’s 1 day’s work = 1/10
Z’s 1 day’s work = 1/50
(x + Y+ Z)’S 1 day’s work = (1/10 + 1/50) = 3/25..........(i)
X’s 1 day’s work = (Y+ Z)’s 1 day’s work.....................(ii)
Solving (i) and (ii), we get
2 * (X’s 1 day’s work) = 3/25
Therefore, X’s 1 day’s work = 3/50
Therefore, Y’s 1 day’s work = (1/10 – 3/50) = 1/25
Therefore, Y alone can do the work in 25 days