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# Tips and Tricks on Time and Work: (Shortcut Methods)

Before going to solve the time and work problems . We need to understand the relation between Time, Work and Manpower (men, women, person, boy , girl etc.,).

Work  α  MDT         [M=Men, D=Days, T=Time]

1) W1  / W2 =  M1D1T1/M2D2T2 .

2) If  W1=W2 Then M1D1T1= M2D2T2.

3) M1D1 / W1 = M2D2 / W2        Here, Time is constant(same)

=> M1D1W2=M2D2W1.

4)M1D1T1E1W2 = M2D2T2E2W1  (E1, E2 are efficiency of the persons in two groups)

## Practice Questions on Time and Work:

Problem 1:

A takes 10 days to complete a work and B takes 5 days to complete the same work. Then, How many days A and B completes the work if they work together?

Sol:   A                           B

10 days                 5 days

Let us assume, Total Work= LCM(10,5)=10 units.

A’s 1day work=10 units/10= 1 unit.

B’s 1day work=10 units/5 = 2 units.

(A+B)’s 1 day work= (1+2)units

= 3 units

(A+B)  total work can be done in Total Work/1day work.

=>10 uits/3units =10/3days.

If we understand the logic in this method, It become very simple to solve other hard problems also in less time.

Problem2:

A->20 days and B->25 days  Then,  (A+B)= ? days.

Sol:    Total Work = LCM(20,25) =100 units.

A’s 1day Work = 100/20 = 5 units

B’s 1 day work = 100/25 = 4 units

(A+B)’s 1 day work = (5+4) = 9 units

(A+B)’s Total work can be done in  Total Work/1 day work=100/9 units

= 11.11 days.                          11 days(approx).

Note: No need to write all these steps .For understanding purpose, I have written here.

Problem 3:

A->5days,  B->7 days,  C->9days   Then, (A+B+C)=? Days.

Sol: T.W= LCM(5,7,9)=(5*7*9 )units

A= (7*9) units

B= (5*9) units

C= (5*7) units

(A+B+C)’s 1 day work= (7*9)+ (5*9) + (5*7)

=63+45+35=143 units.

(A+B+C)’s  completes the work in [(5*7*9 )/ 143 ] days.