General Awareness:--Aptitude Part 4
Time and Work
Time and work, distance aptitude questions are asked in every competitive exam. Placement papers for TCS, Infosys, Wipro, CTS, SSC, GPSC,HCL, IBM or Bank exam or other exams like CAT, XAT, MAT, GRE, GMAT tests always contains one or more aptitude questions from this section of quantitative aptitude.
This article will provide shortcuts, tips and tricks to solve quantitative aptitude questions on time and work.
Basic Concepts and understanding of Time and Work
Analogy between questions on time and work to time, distance and speed:
• Speed is equivalents to rate at which work is done
• Distance travelled is always equivalent to work done.
• Time to travel distance is always equivalent to time to do work.
Man - Work - Hour Formula:
1. More men can do more work.
2. More work work means more time required to do work.
3. More men do more work in less time.
4. M men can do a piece of work in T hours of time, then
Total effort or work =MT man hours
5. Rate of work * Time = Work Done
Rate of work * Time = Work Done
A will do a piece of work in D days, then A's 1 day's work = 1/D
Part of work is done by A for t days = t/D.
6. If A's 1 day's work = 1/D, then A finish the work in D days.
7. If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do w2 work in D2 days working H2 hours per day, then
M1D1H1/W1=M2D2H2/W2
• If A and B together can do a part of work in x days, B and C together can do in y days and C and A together do in z days, then for the same work can be done
By A alone can in 2xyz/(xy+yz-zx) days.
By B alone can in 2xyz/(yz+zx-xy) days.
By C alone can in 2xyz/(zx+xy-yz) days.
By A, B and C can together in 2xyz/(yz+zx+xy) days.
• If the number of men are varied in the ratio of m:n, then the time taken to complete the work will change in the ratio n:m
Examples
1. A completely do a work in 15 days and B in 20 days. If they work on it together for 4 days of time, then the fraction of the work that is left is :
A's 1 day's work = 1/15
B's 1 day's work = 1/20
(A + B)'s 1 day's work will be = (1/15 +1/20) = 7/60
(A + B)'s 4 day's work Will be = (7/60 *4) = 7/15
Therefore, Remaining work is= (1-7/15)= 8/15
2. A, B and C do a part of work in 20, 30 and 60 days respectively. In how many days can alone A do the work if he is assisted by B and C on every third day?
A's 2 day's work=(1/20*2)= 1/10
(A + B + C)'s 1 day's work Will be =(1/20+1/30+1/60)
= (1/10)
Work done in 3 days of time = 1/10 + 1/10 =1/5
Now, 1/5 work is done in 3 days.
Whole work will be done in (3 x 5) of time= 15 days.
3. A and B complete a work in 15 days and 10 days respectively. They started it doing the work together but after 2 days B and have to leave A alone completed the remaining work. The whole work was completed in :
Then (A + B)'s 1 day's part work is to be= (1/15 +1/10) = 1/6
Work done by A and B in 2 days = 1/6 *2 = 1/3
Remaining work =
Now, 1/15 part of work is done by A in 1 day.
2/3 work will be done by a in (15/3*2) = 10 days.
So, the total time taken by them= (10 + 2) = 12 days.
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Aptitude Part 3 :
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