Time and Work Formula: This quantitative topic ‘time and work’ plays an important in any exam like UPSC, State PSC, SSC, etc.
Facts About ‘Time, Work and People’
 People and Work Both are proportional to each other.
 People and Time Both are inversely proportional to each other.
 Time and Work Both are proportional to each other.
 Work done assume 1 always.
Important Rules
 If a man complete his work in X days, then one day work will be 1/X
 When a man’s one day work is 1/X, then he completes his work in X days.
 If X and Y complete a work respectively in A and B days, then they together to finish that work in AB/A+B days, and they will complete together (A+B/AB)^{th} part of work in a day.
 Efficiency (E) ∝ 1/T, (T Time Taken, Amount of work done is constant)
 If one man (X) is E times efficient than the second man (Y), then work done by X:Y = E:1
 If the ratio of the number of working people needed to finish the work is A:B, then the ratio of time consumed by them will be B:A.
Time and Work Formula
 If a man (X) finish work in A days. The second man (Y) finish that works in B days. Then,
 X complete the work in one day will 1/A, Y complete the work in one day will 1/B
 Work done together by X+Y = A+B/AB
 Total time is taken by them = AB/A+B
 When a man (X) finish work in A days. The second man (Y) finish that works in B days. The third man (Z) finish that works in C days. Then,
 X completes the work in one day will 1/A. Y complete the work in one day will 1/B. Z complete the work in one day will 1/C.
 Work done together by X+Y+Z = AB+BC+CA/ABC
 Total time is taken by them = ABC/AB+BC+CA
 If M1 persons complete their W1 work in D1 days and M2 persons complete their W2 work in D2 day works. Then,

 M1*D1*W1 = M2*D2*W2
 M1*D1*W1*T1 = M2*D2*W2*T2 (If time T included)
 M1*D1*W1*T1*E1 = M2*D2*W2*T2*E2 (If efficiency E included)
 When a man (X) alone finish a certain work in A days. But first man (X) and the second man (Y) together finish that work in B days. Then,
The second man (Y) only complete that work in AB/AB days.
 If X and Y finish work in A days, Y and Z finish that work in B days, and Z and X finish that work in C days. Then,
 Total time taken to complete that work together will be 2ABC/AB+BC+CA
 Finished work in one day = Total work/ Total working days
 Total work = Finished work in one day x Total working days
 Work that remains = 1 finished work
 A man (X) that finished a work = One day work x total working days of X.
 Consider, X finished a/b part of work in N days. Then,
 Total time for completing that work by X = (b/a) x N
 Assume, X finished work in A days. Y completed that work in B days. If both started together and Y left the work N days before the completion of work, then
 Consumed total time to finish that work = (B+N)A/A+B
 Consider, X and Y complete work in A days. Both together work for B days. Then,
 When X left that work, then the rest work completed by Y in N days. So, the Total time is taken by Y to complete that work alone = BN/AB.
 When Y left that work, then the rest work completed by X in N days. So, the Total time is taken by X to complete that work alone = AN/AB.
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