- TIME: Means time for completing a job or time actually worked.
- WORK: Means the amount of job assigned or the amount of job actually done.
Results
#1. 4 men and 6 women can complete a work in 8 days , while 3 men and 7 women can complete it in 10 days . In how many days will 10 women complete it ?
4 men and 6 women can complete a work in 8 days , while 3 men and 7 women can complete it in 10 days . In how many days will 10 women complete it ?
1 man’s 1 day’s work = x
1 women’s 1 day’s work =y
Then , 4x add 6y = 1/8 and 3x add 7y = 1/10
x = 11/400 , y = 1/400
1 woman’s 1 days work = 1/400
: 10 woman’s 1 day’s work = ( 1/400 * 10 )
= 1/40
= 40
hence , 10 woman will complete the work in 40 days
#2. If 2 men and 16 boys can do a piece of work in 5 days; 10 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is :
If 2 men and 16 boys can do a piece of work in 5 days; 10 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is :
1 man’s 1 day’s work=x
1 boy’s 1 days work= y
12x plus 16y=1/5
13x plus 24 y= 1/4
x= 1/100
y= 1/200
required ratio = x : y
= 1/100 : 1/200
= 2 : 1
#3. 10 women can complete a work in 7 and 10 children take 14 days to complete the work how many days will 5 women and 10 children take to complete the work?
10 women can complete a work in 7 and 10 children take 14 days to complete the work how many days will 5 women and 10 children take to complete the work?
1 woman’s 1 day’s work =1/70
1 child’s 1 day’s work =1/140
(5 woman plus 10 children)’s 1 day’s work = (5/70 plus 10/140)
= ( 1/14 plus 1/14)
1/7
#4. A alone can complete a work in 16 days and B alone in 12 days. Starting with A, they work on alternate days. The total work will be completed in :
A alone can complete a work in 16 days and B alone in 12 days. Starting with A, they work on alternate days. The total work will be completed in :
(A plus B )’s 2 days work =(1/16 plus 1/12) = 7/48
work done in 6 pairs of days = (7/48* 6)=7/8
remaining work = (1- 7/8)=1/8
work done by A on 13th day= 1/16
remaining work = ( 1/8-1/16)
=1/16
On 14th day it is B’s turn
1/12 work is done by B in 1 day 1/16 work is done byB in (12*1/16)
=3/4 days
total time = 13 3/4 days
#5. 12 men complete a work in 9 days . After they have worked for 6 days more men join them. How many days will they take to complete the remaining work?
12 men complete a work in 9 days . After they have worked for 6 days more men join them. How many days will they take to complete the remaining work?
1 man 1 day’s work = 1/108
12 men 6 day’s work = (1/9 * 6) = 2/3
remaining work = ( 1-2/3)=1/3
18 men’s 1 day’s work (1/108*18)=1/6
1/6 work is done by them in 1 day
1/3 work is done by them in ( 6*1/3)
=2 days
#6. Kim can do a work in 3 days while David can do the same work in 2 days. Both of them finish the work together and get Rs. 150. What is the share of Kim ?
Kim can do a work in 3 days while David can do the same work in 2 days. Both of them finish the work together and get Rs. 150. What is the share of Kim ?
Kim’s wages : David’s wages = Kim’s 1 days work : David 1 day’s wrok
=1/3 : 1/2 = 2 : 3
Kim share = Rs (2/5 * 150)
=Rs. 60
#7. A does 4/5 of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
A does 4/5 of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
whole work is done by A in ( 20 * 5/4)=25 days
(1-4/5)
1/5 work is done by A and B in 3 days
whole work will be done by A and B in 3* 5 = 15 day
A’s 1 days work = 1/25
( A plus B ) 1 days work = 1/15
B’s days work = (1/15- 1/25)
= 4/150
=2/75
37 1/2 days
#8. X can do a piece of work in 40 days. He work at it for 8 days and then y finished it in 16 days. How long will they together take to complete the work
X can do a piece of work in 40 days. He work at it for 8 days and then y finished it in 16 days. How long will they together take to complete the work
work done by X in 8 days = ( 1/40*8) =1/5
remaining work =(1-1/5)=4/5
work is done by Y in 16 days
whole work will be done by Y in ( 16*5/4)= 20 days
X’s 1 days work = 1/40
y’s 1 days work = 1/20
( X plus Y ) 1 days work = ( 1/40 plus 1/20)
=3/40
40/3 = 13 1/3 days
#9. A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forces to leave after 3 days. The remaining work done by A in :
A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forces to leave after 3 days. The remaining work done by A in :
(B Plus C) ‘s 1 days work = (1/9 plus 1/12) =7/36
work done by B and C in 3 days = ( 7 /36 *3)= 7/12
remaining work = (1-7/12)=5/12
1/24 work is done by A in 1 day
5/12 work is done by A in ( 24* 5/12)
= 10 days
#10. A can do a work in 15 days and B in 20 days, If they work on it together for 4 days then ta fraction of the work that is left is :
A can do a work in 15 days and B in 20 days, If they work on it together for 4 days then ta fraction of the work that is left is :
A’s 1 days work = 1/15
B’s 1 days work =1/20
(A plus B )’s 1 days work = ( 1/15 plus 1/20 )
= 7/60
(A plus B )’s 4 days work = ( 7/60 * 4 )
= 7/15
remaining work = ( 1- 7/15)
= 8/15
#11. A is 30 % more efficient then B; how much time will they , working together, take to complete a job which A alone could have done in 23 days :
A is 30 % more efficient then B; how much time will they , working together, take to complete a job which A alone could have done in 23 days :
Ratio of time taken by A and B = 10: 13
suppose B taken X days to do the work
10 : 13 :: 23 : x
X= (23* 13 / 10)
X= 299/10
A’s 1 days work = 1/23
B’s 1 days work = 10 / 299
(A plus B ) as 1 days work = (1/23 plus 10/ 299)
= 23/299
=1/13
A and B together can complete that job in 13 days
#12. A work twice as fast as B; if B can complete a work in 12 days independently the number of days in which A and B can together finish the work is :
A work twice as fast as B; if B can complete a work in 12 days independently the number of days in which A and B can together finish the work is :
A and B = 2: 1
so ratio of time taken = 1 : 2
A’s 1 day’s work =1/6
B’s 1 days work = 1/12
(A plus B )’s 1 days work = ( 1/6 plus 1/12)
= 3/12
= 1/4
=4
A and B together can finish the work is 4 days
#13. A and B can do a work in 8 days B and C can do the same work in 12 days A, B and c together can finish it in 6 days A and C together will do it in :
A and B can do a work in 8 days B and C can do the same work in 12 days A, B and c together can finish it in 6 days A and C together will do it in :
(A plus B plus C )’s 1 day work =1/6
( A plus B )’s 1 days work = 1/8
( B plus C )’s 1 days work = 1/12
(A plus c )’s 1 days work = (2* 1/6)-(1/8 plus 1/12 )
= (1/3-5/24)
= 3/24
=1/8
A and C together will do the work in 8 days
#14. A and B can do a work in 12 days B and C in 15 days C and A in 20 days if A, B , C work together they will complete the work in :
A and B can do a work in 12 days B and C in 15 days C and A in 20 days if A, B , C work together they will complete the work in :
(A Plus B)’s 1 days work = 1/12
( B plus C )’s 1 days work = 1/15
(A plus C)’s 1 days work = 1/20
Adding to both number= 2( A plus B plus C)’s 1 days work = (1/12 plus 1/15 plus 1/20)
= 12/60
= 1/5
( A plus B plus C)’s 1 days work= 1/10
A ,B and C together can complete the work in 10 days
#15. A man can do a piece of work in 5 days but with help of his son he can do it in 3 days in what time son do it alone ?
A man can do a piece of work in 5 days but with help of his son he can do it in 3 days in what time son do it alone ?
son’s a 1 days work = ( 1/3-1/5)
= 2/15
the son can do the work in 15/2= 7 1/2 days
#16. A, B and C can complete a piece of work in 24,6 and 12 days respectively working together they will complete the same work in :
A, B and C can complete a piece of work in 24,6 and 12 days respectively working together they will complete the same work in :
( A plus B Plus C)’s 1 days work = (1/24 plus 1/6 plus 1/12)
= 3/24
A,B and C together will complete the job in 24/7
= 3 3/7 days
#17. Work a taken 8 hours to do a job, worker B taken 10 hours to the same job how long should it take both A and B, working together what independently to do in the same job ?
Work a taken 8 hours to do a job, worker B taken 10 hours to the same job how long should it take both A and B, working together what independently to do in the same job ?
A’s 1 hours work =1/8
B’s 1 hours work =1/10
(A plus B)’s 1 hours work = ( 1/8 plus 1/10)
= 9/40
4 4/9 days
#18. A can do a certain job in 12 days , B is 60 % more efficient then A how many days does B alone taken to do same job?
A can do a certain job in 12 days , B is 60 % more efficient then A how many days does B alone taken to do same job?
Ratio of time taken by A and B = 160 : 100
= 8 : 5
suppose B alone takes X days to do the job
8 : 5 :: 12 : X
8 x = 5* 12
x= 7 1/2 days
#19. A job can be done by 3 skilled workmen in 20 days or by 5 boys in 30 days . How many days will they take if they work together?
A job can be done by 3 skilled workmen in 20 days or by 5 boys in 30 days . How many days will they take if they work together?
job of 3 skilled men in 20 days = job of 5 boys in 30 days
time = 20 * 30/ 20 plus 30
= 12 days