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# Time And Work

It is very important for a candidate is to aware of the basics concept and the types of questions that may be asked in the competitive exams, mainly banking and SSC exams.

“Time and work” topic deals with the time taken by an individual or a group to complete a job or a piece of work and its efficiency of them.

Question Patterns:-

1) To find the efficiency of an individual or a group
2) To find the time taken by a person or a group to do a piece of work or a job.
3)  A certain work done by an individual in a certain time period
4) A certain work done by a group of individuals in a certain time period
5) To find wages.

Important Formula:

The formulas can completely help you to do a solution as soon as you read the question. Thus, it makes the solution and the related calculations simpler.

1. Work Done by a person = Time Taken × Rate of Work

2. Rate of Work of a person  = 1 / Time Taken by him

3. Time Taken by him = 1 / Rate of Work

4. If a piece of work or a job is done in n number of days, then the work done in one day = 1/n

5. Total Work Done = Number of Days × Efficiency

6. Efficiency of work done and Time are inversely proportional to each other.

7. M : W is the ratio of the number of men and women which are required to complete a piece of work, then the ratio of the time taken by them to complete the work will be W : M.

8. If W1 work is done by M1 people in D1 days, working T1 hours in a day and W2 work is done by M2 people in D2 days, working T2 hours in a  day, then the relation between them will be
(M1 × D1 × T1 × W2) = (M2 × D2 × T2 × W1)

Questions Related to Time and Work:

1. Question
A man can do a work in 20 days and a woman in 15 days. If they work on it together for 5 days, then the fraction of the work that is left is :

A. 1/12
B. 1/10
C. 5/12
D. 7/15
E.  8/15

Explanation:

Man’s 1 day’s work = 1/20
Woman’s 1 day’s work = 1/15
(Man + woman)’s 1 day’s work = (1/20 + 1/15)  = 7/60
(Man + woman)’s 5 day’s work = (7/60 × 5) = 7/12
Thus, Remaining work = 1 – 7/12 = 5/12

2. Question
L can finish a work in  16 days and M can do the same work in 12 days. With help of N, they did the work in 4 days only. Then, N alone can do the work in how many days.

A. 48/5 days
B. 48/7 days
C. 48/11 days
D. 10 days
E.  None of these

Explanation:

(L + M + N)’s 1 day’s work =1/4
L’s 1 day’s work = 1/16
M’s 1 day’s work = 1/12
Therefore, N’s 1 day’s work
= 1/4 – (1/16 + 1/12)
= 1/4 – 7/48
= 5/48

So, N alone can do the work in 48/5 days.

3. Question
P, Q and R can do a job in 20, 30 and 60 days respectively. In how many days can P do the job if he is assisted by Q and R every third day?

A. 11 days
B. 15 days
C. 17 days
D. 16 days
E. 18 days

Explanation:

P’s 2 day’s work = 2/20 = 1/10
(P + Q + R)’s 1 day’s work
= (1/20 + 1/30 + 1/60)
= 6/60   = 1/10
Job done in 3 days = (1/10 + 1/10) = 1/5
Now, 1/5 jobs is done in 3 days
Whole job  will be done in (3 x 5) = 15 days.

4. Question
M’s efficiency is three times N’s efficiency. M can finish a job in 60 days less than N. If they work together, then in how many days the job will be done.

A. 20 days
B. 22.5 days
C. 25 days
D. 30 days
E. 24.5 days

Explanation:

The ratio of times taken by M and N = 1 : 3   (Since the efficiency of M is three times to N)

The time difference is (3 – 1) = 2 days, while N take 3 days and M takes 1 day.

2 units = 60 days
1 unit = 30 days

So, M takes 30 days to do the job.
And N takes (30×3) = 90 days to do the job.

M’s 1 day’s work = 1/30
N’s 1 day’s work = 1/90
(M + N)’s 1 day’s work =( 1/30 + 1/90) = 2/45
M and N together can do the job in 45/2 days = 22.5 days

5. Question
Ankit alone can do a piece of work in 6 days and Bishal alone in 8 days. Ankit and Bishal undertook to do it for Rs. 4800. With the help of Dinesh, they completed the work in 3 days. How much is to be paid to Dinesh?

A. Rs. 1375
B. Rs. 1400
C. Rs. 1600
D. Rs. 1800
E.  Rs. 2000

Explanation:

Ankit’s 1day work = 1/6
Bishal’s 1 day work = 1/8
(Ankit + Bishal + Dinesh)’s 1 day work =1/3
Dinesh’s 1 day work = 1/3 – (1/6+1/8) = 1/24
Ankit’s wages : Bishal’s wages : Dinesh’s wages
=1/6 : 1/8 : 1/24.

Here the (LCM of 6,8 and 24) is 24. Now, taking LCM we get ratio
= 4 : 3 : 1
Dinesh’s share (for 3 days) = 3 × 1/8 × 4800 = 1800

6. Question

Vicky completes a job in 45/2 days. What part of the job will he do in 2 days?

A) 4/45

B) 1/45

C) 2/45

D) 8/45

E) 1/15

Explanation:-

We know, if a person does a job in n days, then his 1-day work = 1/n

Here, n = 45/2

Vicky’s 1-day work = 2/45

Thus, Vicky’s 2 days work = 2× 2/45 = 4/45

7. Question

Karan completes 1/15 part of a certain job in 1 day. In how many, he will complete the full job.

A) 30 days

B) 15 days

C) 20 days

D) 5 days

E) 10 days

Solution:-

Here, 1/n = 1/15

So, n = 15

Thus, the required days = 15

8. Question
In a factory, 20 people can make 20 toys in 15 days working 10 hours per day. Then, in how many days can 25 persons make 30 toys working 20 hr per day?

A) 6 days
B) 9 days
C) 10 days
D) 12 days
E) 15 days

Explanation:-
Here, M1 = 20, M2 = 25, D1 = 15, D2 =? , T1 = 10 , T2= 20, W1 = 20 and W2 = 30.
We know,
M1 × D1 × T1 × W2 = M2 × D2 × T2 × W1
=> 20 × 15 × 10 × 30 = 25 × D2 × 20 × 20
=> D2 = 9.
Thus, the required day = 9 days

9. Question
23) P, Q and R together can complete a work in 16 days and R alone complete the work in 20 days. If P, Q and R started the work together and after 10 days P and Q left the work, in how many days R alone complete the remaining work?

a) 12½ days
b) 20½ days
c) 4 days
d) 7½ days
e) 15 days

Explanation:

P + Q + R = 16 days
R =20 days
Total work (LCM of 16 and 20) = 80
( P + Q +R) ‘s work
= 80 /16
= 5 unit
Work done by R = 80 /20 = 4 unit
(P + Q + R) ‘s 10 days work
= 5 × 10
= 50 unit

Remaining work
= (80 – 50)
= 30 unit
Remaining work done by R
= 30/4
= 7½ days

10. Question
M did a piece of work in 5 days. That piece of work was done by N in 9 days. If M and N worked together, they got total wages of Rs 4200. Find the share of N.

a) 1500
b) 2000
c) 1000
d) 1200
e) None of these

Explanation :-
M   :  N
Time   =           5    :  9
Efficiency=      9    :  5
(Time and efficiency are inversely proportional)
N gets = 4200 ×  5/14
= 1500
Thus, N gets the wages of Rs 1500.

11. Question
P and Q can do a job in 3 days. Q and R can do the same job in 9 days, while R and P can do it in 12 days. In how many days the job will be finished when P, Q and R working together.

A) 72/19 days
B) 83/10 days.
C) 61/3 days.
D) 67/4 days
E) None of these

Explanation:

Here, (P + Q)’s 1 day’s work = 1/3
(Q + R )’s 1 day’s work= 1/9

and (R + P)’s 1 day’s work = 1/12

Now, 2 (P + Q + R)’s 1 day’s work = (1/3+1/9+1/12)
= 19/36

(P + Q + R)’s 1 day’s work = 19/(36 ×2)=19/72

Hence, (P + Q + R) complete the work in= 72/19 days

12. Question
E and F are two friends working together to finish a work in 24 days and E alone can do the same work in 36 days. In how many days can F alone complete the work?

A) 36 days
B) 24 days
C) 72 days
D) 48 days
E) None of these

Explanation :
(E+F)’s 1 days work = 1/24
E’s 1-day work = 1/36
F’s 1 day work = (1/24 – 1/36)  = 1/72
Thus, the time is taken by F to finish the work alone= 72 days

13. Question
If 12 men or 18 boys can build a wall in 48 days, then how long will 6 men or 9 boys build the wall?

A) 48 days
B) 36 days
C) 64 days
D) 72 days
E) 96 days

Explanation :
12 men = 18 boys
2 men = 3 boys
Now, 12 men + 2×18/3 men = 24 Men
And, 6 men + 2× 9/3 men = 12 men
Here, M1 = 24, M2 = 12, D1 = 48, D2 =?
According to the formula,
M1 × D1 = M2 × D2
=> 24 × 48 = 12 × D2
=> D2 = 96

14. Question
Akash can reap a field in 45 days and Vishal is 200% more expert than Akash to reap the field, then find total time taken to reap the field by Vishal.

A) 15
B) 20
C) 22
D) 25
E) 30

Explanation:
According to the question, Vishal is more efficient than Akash. So, he takes less days to complete the work.

Let, Vishal takes time = x days
So, Akash takes time = 3x days
According to the question,
3x = 45
x = 15
Thus, Vishal takes time 15 days.

15. Question
Two brothers(younger and older) can do a piece of work in 70 and 60 days respectively. They began to work together, but the younger brother leaves after some days and the older brother finished the remaining work in 47 days. After how many days did the younger brother leave?

A) 14 days
B) 16 days
C) 11 days
D) 12 days
E) 7 days