TIME AND WORK

More than two questions are asked from this area in ail exams. So studying this topic in detail is a must so that your rank will be higher than others.

TYPE-I

1.If a person can do a piece of work in 'n' days, work done by him in one day = 1/n
2.If work done by a person in one day is' / n 'then he 030 finish the whole work in'n'days.
3. If Mx persons can do W1 works in D1 days for T1 hours and M2 persons can do W2 works in D2 days for T2 hours, then.
M1D1T1W2 = M2D2T2W1

EXAMPLES

1.If 20 men can complete a piece of work in 10 days, then how many men are required to complete the work in 50 days.
= M1D1T1W1 =M2D2T2W1
there, W1= W2 = 1
20 x 10 = M2 x 50
M2 = 4
4 men are required to complete the work in 50 days.
2.40 men can cut 50 trees in 5 hours. If 4 men leave the job, how many trees will be cut in 9 hours?
M1D1W2T1=M2D2W1T2
40*5*W2=36*9*50
W2 = 36*9*50/40*5=81
.'.No. of trees cut = 81

TYPE-II

1.If A can finish a work in 'x' days and B can finish the same work in  days, then A and B together can finish the work in
XY/XYdays.
2.If A and B together can do a piece of work in 'x' days and A alone can do the work in y days, then B alone can do
the work in XY/Y-Xdays.
3.If A, B and C can do a work in x,y and z days respectively, then A, B and C together can complete the work in
XYZ/XYYZXZ days

EXAMPLES

1.

If Vimal can do a work in 6 days and Ansar can do the same work in 3 days, then in how many days they together can do the work.
xy/xy = 6x3/63=18/9=2
.'. They together can complete the work in 2 days.

2.

If A and B together can do a piece of work in 6 days and B alone can do the work In 18 days, then how many days will A take to complete the work.
(A  B)'s one day's work = 1/6
B's one day's work =1/18
A's one day's work =1/6 -1/18
=2/18=1/9
ie, 9 days
.'.A can complete the work in 9 days 
OR
xy/y-x=6 xl8/18-6= 6x18/12=9 days

3.

A and B can do a piece of work in 12 days B and C can do it in 20 days, while A and C can do it in 15 days.
(a)In how many days will they all working together can finish the work.
(b)In how many days B alone can do the work.
(a) (A  B)'s one days work =1/12
(B  C)'s one days work =1/20
(A  C)'s one days work = 1/15
2(A  B  C) one days work
=1/12  1/20  1/15
=12/60=1/5
.'.(ABC) one day's work = 1/5*2=1/10
.'.A, B & C together can complete the work in 10 days.
(b) B's one day's work = (ABC)'s one day's work - (CA)'s one day's work 
=1/10-1/15=5/150=1/30
.'.B alone can complete the work in 30 days.

TYPE-III

1.If A is twice efficient a workman than B, then the ratio of work done by A and B is 2:1, whereas the ratio of time taken by A and B is 1:2.
2.If A is 'K' times as good a workman than B, then A will complete a job in 1/K of the time taken by B to complete that job.

EXAMPLES

1.

A can do some work in 10 days. B is 50% more efficient than A. Then in how many days B alone can do the same work.
Efficiency of A and B is in the ratio = 100 : 150 = 2:3
.'.Number of days are in the ratio =>3:2
3:2 =10 : x
3/2 =10/x
3x =20
x =6.66 OR 6 2/3 days
.'.B alone can do the work in 6.66 days.

2.

A and B are working in the same company. A is 30% more efficient than B. A alone can do work in 23 days. If A and B work together how much time will they take to finish the work.
Given A : B = 100 : 130 = 10 : 13 
Let B takes x days to do the work 
Then, 10 : 13= 23 : x
=>x=23x13/10=299/10
(A)'s one day's work = 1/23 
(B)'s one day's work = 10/299
.'.(AB)'s one day's work
=[1/2310/299]=23/299=1/13

3.

A is twice as good a workman as B and hence is able to complete a work in 60 days less than B. If A and B work together, in how many days will they complete it.
Let A takes x and B takes 2x days to complete the work 
Given, 2x - 60= x
x =60 days
.'.(B)'s time to complete the work = 2x 
= 2 x 60 = 120 days.
.'.(AB)'s one day's work
=1/60 1/120 =3/120 =1/40
.'.A and working together can complete the work in 40 days.

PRACTICE EXERCISES

1.15 men can do a piece of work in 30 days.How many days are required to complete this work if 6 men do this work.
2.If A does some work in 20 days and B does the same work in 15 days,in how many days they together will do the same work
3.P and Q can do some work in 8 days.When they work together.Q alone can do it in 12 days.Q left the work after 6 days.Ho many days will P take to complete the remaining work
4.A and B can together do a piece of work in 20 days and A alone can do it in 40 days.In how many days B alone can do it.
5.If A can do some work in 9 days,B in 15 days and C in 45 days,how long will they take to complete the work if they work together.
6.If 6 men and 8 boys can do a piece of work in 10 days while 26 mn and 48 boys can do the same in 2 days,the time taken by 15 men and 20 boys in doing the same type of work will be __
7.Rajan & Kishor are working on an assignment. Rajan takes 6 hours to type 32 pages on a computer, while Kishor takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages.
8.Manju can do some work in 20 days. Mini is 25% more efficient than her. In how many days Mini can complete the same work.
9.A can finish a work in 24 days, B in 9 days and C in 12 days. B and C started the work but left after 3 days. A alone can do the remaining work in how many days. 
10.P and Q can do a work together in 7 days. Pis 1 3/4 times as efficient as Q. In how many days, P alone can do this work.

ANSWERS WITH EXPLANATION

1.

M1D1W2= M2D2W1
=>15x30x1= 6 x D2 x 1 
.'.D2 = 75
.'.Required answer=75 days

2.

xy/x  y 
20x15/2015=60/7=8 4/7
.'.Together they will complete the work in 60/7 days

3.

(AB)'s one day's work =1/8
(B)'s one day's work = 1/12
.'.(A)'s one day's work =1/8 -1/12
=3-2/24 =1/24
.'.A can complete the work in 24 days
Now,(B)'s 6 day's work=6*1/12=1/2
Remaining work = 1-1/2=1/2
Time taken by A to 1/2 of the work
= 1/2*24=12 days

4.

xy/y-x
=20x40/40-20 = 20x40/20 =40
.'.B alone can do the work in 40 days 

5.

xyz/xy  yz  xz
=9x15x45/(9xl5)(l5x45)(9x45)
=9x15x45/135675405
=9*15*45/1215=5
.'. They together can complete the work in 5 days.

6.

Let 1 man's 1 day's work = x and 
1 boy's 1 day's work = y
Then, 6x  8y = 1/10 and 
26x  48y= 1/2
Solving => x = 1/100 and y =1/200
(15 men 20 boy's) 1day's work
=[15/100  20/200] = 1/4
...15men and 20 boys can do the work in 4 
days.

7.

no.of pages typed by Rajan in 1 hour
=32/6 = 16/3
No.of pages typed by Kishor in 1 hour
= 40/5 = 8
No.of pages typed by both in 1 hour
=[16/3  8] = 40/3
...Time taken by both to type 110 pages
=[110*3/40]hours

8.

Ratio of times taken by Manju and Mini
=125 : 100 =5:4
Let mini takes *days to do the work
5:4::20:x
x = 4*20/5 = 16
...Mini takes 16 days to complete the work.

9.

(BC)'s one day's work
=[1/91/12]=7/36
work done by B and C in 3 days
=7/36*3=7/12
Remaining work = 1-7/12 = 5/12
Now,1/24work is done by A in one day
So 5/12 work is done by A in (24*5/12)
days = 10days

10.

p's One day's work : Q's one day's work
=7/4 :1 = 7:4
Let P's one day's work be 7x and
Q's one day's work be 4x
Then,7x  4x = 1/7
11x=1/77
...p's one day's work = 1/77*7=1/11
...p alone can do the work in 11 days.