Time and Work Formula for UPSC, State PSC, SSC Exams

By | October 22, 2020

Time and Work Formula: This quantitative topic ‘time and work’ plays an important in any exam like- UPSC, State PSC, SSC, etc. 

Time and Work Formula

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/A-B 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/A-B.
  • 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/A-B.

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