##
** Time and Work - Concept**

Performing
any work or task involves efforts of Men over a period of time. Therefore the
important variables in problems related to time and work are , the
number of men (M) and the period of time to complete the work (W) and
quantity of work (W) to be perfomed.

The
time taken to perform a work not only depends on the number of men, but also
depends on the efficiency of the men involved in the work.

In
this chapter, time period taken to finish the work is usually given in number
of days. But in some cases, in addition to the number of days, the number of
hours per day that the man is working also given.

**Important Points to be remembered:**

**1.**If a person can do a work in N days, in 1 day he can do

1
N

of the the work
Example
: Ramesh can do a work in 15 days , then in 1 day he can do

1
15

th of the work**2.**If a man can do

1
N

of the work in a day , he can complete the total work in N
days
Example
: If Ramesh can do a

1
8

th work in a day ,
he can complete the total work in 8 days .**3.**If M men can do a work in N days , in 1 day, 1 man can do

1
M X N

of the work
Example:
If 20 men can do a work 30 days, then 1 man can do the same work in

1
20 x 30

=
1
600

th of the work**4.**If M men can do a work in N days, then 1 man can do the same work in M X N days

Example
: If 10 men can do a work in 5 days , the time required to perform the work by
1 man = 10 x 5 = 50 days

**5.**Number of Man days (Work days)= Number of Men x Number of days

Example
: If 15 men can do a work in 8 days, then number of Man days = 15 x 8 = 120
days

Number
of days required by one man to finish the work is Number of man days.

**6**. If the ratio of time taken by A and B in doing a work = m : n, then the ratio of work done by A and B =

1
m

:
1
n

= n :m
Example
: A and B can do a work in 30 days and 20 days respectively , then the ratio of
work done by A and B = 30 : 20 =3 : 2

**7.**The wages are always distributed based on the ratio of the efficiencies of people involved in the work.

If
the ratio of time taken by A and B in performing a work is m :n , the ratio of
their efficiencies is n :m. So the wages are distributed in the ratio n:m

**Example :**A and B can do a work in 20 days and 25 days respectively. They got a remuneration of Rs 1800. What is the share of B ?

**Explanation :**The ratio of times taken by A and B is 20 :25 = 4 : 5

So the ratio of
their efficiencies = 5 :4

The ratio of the distribution of wages must be 5 : 4

The share
of B = Rs 1800 x

4
9

= Rs 800**8.**If three men can a work in x,y and z days

-> the ratio of their efficiency=

1
x

:
1
y

:
1
z

-> the ratio in which the wages are distributed =

1
x

:
1
y

:
1
z

Example: A , B and C can do a work in 10,12 and 15
days respectively. What is the share B in the total wages Rs 4500?

The ratio of times taken by A, B and C is

1
10

:
1
12

:
1
15

So the ratio of
their efficiencies = 6:5:4

The ratio of the distribution of wages must be 6: 5 : 4

The share
of B = Rs 4500 x

5
15

= Rs 1500**9.**If A is n times more than B,i.e, A has n times capacity to do work that the capacity of B. A will take

1
n

of the time taken by B to do the same amount of
work.**10.**The number of men involved to do a certain work t o be changed in the ration M1:M2, the time required to do the same work will changed to its inverse ratio i.e, M2 :M1.

Example: If the number of men engaged to perform a
certain work be increased in the ration 2:3, the time required to finish the
work will decrease in the ratio 3:2.

**11.**If A is

X
Y

times as a good a workman as B, the A will take
Y
X

of the time
that B takes to perform the work.**Relationship between the three variables i.e, the amount of work (W), the number of men (M) and the time taken to finish the work (T) :**

**12.**More work required more men : If the time to complete the work remains unchanged and vice versa , (Time is constant), then amount of work (W)is directly proportional to number of men (M)

M ∞ W Where T is
constant

**13.**More work required more time and vice –versa : If the number of men engaged to complete the work remains unchanged ( M is constant), then amount of work (W) is directly proportional to the time (T)

W ∞ T , where M is constant

**14.**If amount of work (W) remains unchanged, more number of men (M) will take less time (T). M and T have inversely proportional relationship.

M ∞

1
T

, where W is constant
Combining
all these, we get the important relationship

M1 T1
W1

=
M2 T2
W2

**Very important and useful relationship:**

**15.**If M1 men can do a work W1 in D1 days working H1 hours a day, and M2 men can do same kind of work W2 in D2 days working H2 hours a day , then

M1 D1 H1
W1

=
M2 D2 H2
W2

For more question on time and work , visit

**Time and Work Solved Problems**

**For questions asked in TCS on time and work , visit TCS placement questions on Time and Work**