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

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/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.