Time and work
1. A can do piece of work in 30 days while B alone can do it in 40 days. In how many days can A and B working together do it?
Answer with Explanation:
A can finish his work in 30 days
B can finish his work in 40 days
There fore A’s one day’s work = 1/30
B’s one days work = 1/40
(A+B)’s one day’s work is = 1/30 + 1/40
= - 7/120
A and B together finish the work =
= 120/7
= 17 1/7 days
2. A and B together can complete a piece of work in 35 days while A alone can complete the same work in 60 days. B alone will be able to complete the same working in ?
ANswer with Explanation:
A and B finish one work with company = 35 days
(A + B)’s one days work = 1/35
A alone finish the same work = 60 days
A’s one day’s work = 1/60
B’s one day’s work = (A + B)’s one days work - A’s one day’s work
= -
= = = 1/84
B alone can complete the work = 84 days
3. A can do a piece of work in 7days of 9 horse each and B can do it in 6 days of 7 hours each. How long will they take to do it, working together 8 2/5 hours a day ?
Answer with Explanation:
A do a work for 1 day = 9 hours
For 7 days = (7x9) hours = 63 hours
B can do a work for 1 day = 7 hours
For 6 days = 42 hours
A do a work = 63 hours A’s one hou’s work = 1/63
B do a work = 42 hours B’s 1 hour’s work = 1/42
(A+B)’s 1 hour’s work = + (take LCM)
= =
(A+B)’s working hours = 126/5
Number of days 8 2/5 hours each = = x = 3
Answer = 3 days
4. A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and them leaves. A alone can finish the remaining in
Answer with Explanation:
B finish the work within 10 days ( a work)
in 5 days the finishing value of work = 1/10 x 5 = ½
Remaining work = 1- ½ = ½
A can do a work in 15 days ( one work)
A do a half work = 15/2 days = 7 ½ days
5. A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10 days in how many days both A and B toether can do the wrok
ANswer with Explanation:
A can do 1/3 of work in = 5 days
Whole work done by A = 5 x 1/3 = 15 days
B do 2/5 of work in = 10 days
Whole work done by B = 10 x 5/2 = 50/2 = 25 days
A’s one day work = 1/15
B’s one day work = 1/25
(A+B)’s 1day’s work = + (take LCM)
= =
(A+B) can finish their work in 75/8 = 9 3/8 days.
6. A can do a piece of work in 80 days. He works at it for 10 days and then B alone finished the remaining work in 42 days. The two togther could complete the work in ?
Answer with Explanation:
A’s 10 days work = 1/80 x 10 = 1/8
Remaining work = 1 – 1/8 = 7/8
7/8 part of awork done by B in 42 days
whole work will be done by B in 42 x 7/8 = 48 days
Now A’s one days work = 1/80
B’s one day’s work = 1/ 48
(A+B)’s 1day’s work = +
= = = 1/30
A and B finish the work in 30 days.
7. A and B can together finish a work in 30 days. They workd at it for 20 days and then B left. The remaining work was done by A alone in 20 more days A alone can finish the work in
Answer with Explanation:
A and B’s one day’s work = 1/30
A and B’s 20 day’s work = 1/30 x 20 = 2/3
Remaining work = 1-2/3 = 1/3
Now 1/3 part of work done by a in 20 days
Whole work will be done by a in 20 x 3/1 = 60 days.
8. A and B can do a piece of work in 45 days and 40 days respectively. They began to go the work together but A leaves after some days and than B completed the reaminnig work in 23 days. The number o days after which A left the work was
Answer with Explanation:
A’s one day’s work = 1/45
B’s one day’s work = 1/40
(A+B)’s 1day’s work = + (take LCM)
= =
Work done by B in k23 days = 1/40 x 23 = 23/40
Remaining work = 1 – 23/40 = = 17/40
(A+B)’s 1day’s work =
17/40 work done by (A + B) in 1 x 360/17 x 17/40 = 9 days.
9. A does half as much work as B in three fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it ?
Answer with Explanation:
Let A takes x days to do the work
A takes ( 2 x ¾ x) = 3x/2 days to do work.
But given (A + B)’s 1 days work = 1/18
+ = 1/18
+ = 1/18
=
Cross multiply
(3+2) 18 = 3x
90 = 3x
X = 30
B takes 30 days to do the work.
10. A can do a certain job in 12 days. B is 60% more efficient than A . The number of days, it takes B to do the same piece of work is ?
Answer with Explanation:
Given B is 60% more than A
Assume A is 100 because percentage
B is 60 + 100 = 160
Ratio of times taken by A and B = 160 : 100 = 8:5
Now assume B take days x
Given A do the job = 12 days
The ratio is 12 : x
Comparing 8 : 5 :: 12 : x (apply above basic formula ad = bc)
8x = 60
X = 60 / 8 = 7 ½ days
B takes 7 ½ days to do the same piece of work.
11. A can do a certain job in 25 days which B alone can do in 20 days. A stared the work and was joined by B after 10 days. The number odays tkane in completing the work was
Answer with Explanation:
A’s one day work = 1/25
B’s one day work = 1/20
(A+B)’s one day’s work = 1/25 + 1/20 = 9/100 (take LCM)
A alone do the work for 10 days
A’s work value is 1/25x10 = 2/5
Remaining work is (1- 2/5) = 3/5
Now, 9/100 work is done by both in 1 day
3/5 work will be done by both in 100/9 x 3/5 x 1 = 20/3 days
Already given A do for 10 days
Total time is 10 + 20/3 = 50/3 = 16 2/3 days.
12. A is twice as good a work man as B and together they finish a piece of work in 14 days The number of days taken by A alone to finish the work.
Answer with Explanation:
Given A is twice as like as B
take x for B and 2x for A
we get (A’s one day’s work) : (B’s one day’s work) = 2:1
But given (A+B)’s one day’s work = 1/14
Divide 1/14 in the ratio 2:1
A’s one day’s work = 1/14 x 2/3 = 1/21
A alone can do the work in 21 days.
13. A is thrice as good a workman as B and Takes 10 days less to do a piece of work than B takes.B alone can do the while work work in :
Answer with Explanation:
Given A is 3 times as like as B
Ratio of time taken by A and B = 1:3
Since, the ratio is 3:1
Ratio of time for the part is 1/3 : 1/1 (cross multiply)
Ratio of time for the both is 1:3
Now, if the difference of time is 2 days, B takes 3 days
If the difference of time is 10 days, B takes 3/2 x 10 = 15
B alone do the work in 15 days.
14. A can do a piece work in 14 days which B can do in 21 days. They being together but 3 days the completion of the work. A leaves of the total number of days to complete the work is
Answer with Explanation:
A’s one day’s work = 1/14
B’s one day’s work = 1/21
(A+B)’s 1day’s work = + (take LCM)
= =
Now, 5/42 work is done by A and B in 1 day. B’s 3 day’s work = 3/21 =1/7
Remaining work = 1/1/7 = 6/7
6/7 work is done A and B in (42/5 x 6/7 x 1) = 36/5 days
Already B done the work for 3 days
The total time is 3 + 36/5 = = 51/5 = 10 1/5 days
15. If ramesh, suresh and hairsh can do a piece of work in 15 days, 10 days and 6 days respectively. How long will they take to do it, if all the three work it together?
Answer with Explanation:
Given Ramesh’s one day’s work = 1/15
Suresh’s one day’s work = 1/10
Harish’s one day’s work = 1/6
(Ramesh + Suresh + Harish)’s one day’s work = + + (take LCM)
= = 1/3
if all the three finish the work in 3 days.
16. A and B can do a piece of working 72 days : B and C and do it in 120 days ; A and C can do it in 90 days. In what time can A alone do it ?
Answer with Explanation:
Given (A+B)’s one day’s work = 1/72
(B+C)’s one day’s work = 1/120
(C+A)’s one day’s work = 1/90
Adding these three
(A+B) + (B+C) + (C+A) = 2 ( A+B+C)
2 ( A+B+C) ‘s 1 day’s work = 1/72 + 1/120 + 1/90 (take LCM 720)
= = 1/30
(A+B+C) ‘s 1 day’s work = 1/30 x ½ = 1/60
A’s one day’s work = (A+B+C) - (B+C)
= 1/60 – 1/120 = 1/120
A alone do the work for 120 days.
17. A and B and C together can finish a piece of work in 4 days: alone can do it in 12 days and B in 18 days, then C alone can do it in :
ANswer with Explanation:
Given (A+B+C) ‘s 1 day’s work = ¼
A’s 1 day’s work = 1/12
B’s One day’s work = 1/18
(A+B)’s one day’s work = 1/12 + 1/18 (LCM =36)
= = 5/36
C’s one day’s work = (A+B+C)’s one day’s work – (A+B)’s 1 day’s work
= ¼ - 5/36
= = 4/36 = 1/9
C alone can do it in 9 days
18. A and B can do a piece of work in 18 days: B and C can do it in 24 days : A and C can do it in 36 days. In how many days can they do it all working together?
Answer with Explanation:
Given (A+B)’s one day’s work = 1/18
(B+C)’s one day’s work = 1/24
(C+A)’s one day’s work = 1/36
Adding these three
(A+B) + (B+C) + (C+A) = 2 ( A+B+C)
2 ( A+B+C) ‘s 1 day’s work = 1/18 + 1/24 + 1/36 (take LCM 72)
= = 1/8
(A+B+C) ‘s 1 day’s work = 1/8 x ½ = 1/16
Altogether can do their work in 16 days.
19. A is twice as good as workman as B and together they complete a work in 15 days . in how many days can the work be complete by B alone
Answer with Explanation:
Given A is twice as like as B
(A’s one day’s work): (B’s one day’s work) = 2:1
Again given (A+B)’s 1 day’s work = 1/15
B’s one day’s work = 1/3 X 1/15 = 1/45
B alone can complete the work in 45 days.
20. 45 men can complete a wok in 16 days. Six days after they started working 30 more men joined them. How many days will they now take to complete the remaining work?
Answer with Explanation:
(45 x 16) men can complete the work in one day
1 man’s one day’s work = = 1/720
45 men’s 6 days work = 1/16 x 6 = 3/8
Remaining work = 1 – 3/8 = = 5/8
45 + 30 = 75 men’s one day’s work = 75/720 = 5/48
Now 5/48 work is done by them in one day
5/8 work is done by them in (48/5 x 5/8 x 1) = 6 days.
21. 12 men can complete a work in 18 days six days after they started working men joined them. How many days will all of them together complete the remaining work? Answer with Explanation:
(12 x 18) men can complete the work in 1 day
1 man’s 1 day’s work = =
12 men’s 6 day’s work = 1/18 x 6 = 1/3
Remaining work = 1 – 1/3 = = 2/3
Now 16 men’s 1 day’s work = 16/216 = 2/27
2/27 work is done by them in 1 day
2/3 work is done by them in ( x x 1) = 9 days.
22. Twelve men can complete a work in 8 days. Three days after started the work 3 more men joined. In how many days will all of them together complete the remaining work
Answer with Explanation:
Given 12 men can done a work in 8 days
1 man’s 1 day’s work = = 1/96
12 men’s 3 day’s work = 1/8 x 3 = 3/8
Remaining work = 1 - = =
15 men’s 1 day’s work = 15/96
Now 15/96 work is done by them in 1 day
5/8 work is done by them in ( x x 1) = 4 days.
23. A,B and C are employed to do apiece of work for Rs.529. A and C are supposed to finish 19/23 of the work together. How much shall be paid to B?
Answer with Explanation:
Given (A +C)’s one day’s work = 19/23
B’s alone do the work = 1- = = 4/23
(A +C) : B = 19/23 : 4/23 = 19 : 4
B’s Share = Rs. (529 x 4/23) = Rs. 92/-
24. A job is completed by 10 men in 20 days and by 20 women in 15 days. The days will it take for 5 men and 10 women to finish that work?
Answer with Explanation:
Let 1 man’s one day’s work = x
1 woman’s one day’s work = y
Then 10x = 1/20 and 20y = 1/15
So, x = 1/200 and y = 1/300
(5 men + 10 women)’s one day’s work = 5/200 + 10/300 (LCM = 600)
= = 7/120
They will finish the work in 120/7 = 17 1/7 days.
25. A and B can do a piece of work in 5 days. B and C can do it in 7 days, A and C can do it in 4 days. Who among these will take the least time if put to do it alone?
Answer with Explanation:
Given (A+B)’s one day’s work = 1/5
(B+C)’s one day’s work = 1/7
(C+A)’s one day’s work = 1/4
Adding these three
(A+B) + (B+C) + (C+A) = 2 ( A+B+C)
2 ( A+B+C) ‘s 1 day’s work = 1/5 + 1/7+ 1/4 (take LCM 140)
= (A+B+C) ‘s 1 day’s work = x ½ = 83/280
Now A’s one day’s work = (A+B+C) ‘s 1 day’s work - (B+C)’s one day’s work = 83/280 – 1/7 = =
B’s one day’s work = (A+B+C) ‘s 1 day’s work - (C+A)’s one day’s work = 83/280 – 1/4 = =
C’s one day’s work = (A+B+C) ‘s 1 day’s work - (A+B)’s one day’s work = 83/280 – 1/5 = = Time taken by A, B, C is 280/43 , 280/13, 280/27 days respectively.
The time taken by A is least.
26. A and B take 8 days, B and C 12 days. A, B and C take 6 days. A and C take
Answer with Explanation:
Given (A+B)’s one day’s work = 1/8
(B+C)’s one day’s work = 1/12
(A+B+C) ‘s 1 day’s work = 1/6
A alone can do the work = (A+B+C) ‘s 1 day’s work - (B+C)’s one day’s work
= 1/6 – 1/12 = =
C alone do the work = (A+B+C) ‘s 1 day’s work - (A+B)’s one day’s work
= 1/6 – 1/8 = =
(A+C)’s one day’s work = + = = =
(A+C) can take 8 days to complete the work together.
27. A and B take 12 days, B and C 15 days, C and A 20 days. A, B and C together take:
Answer with Explanation:
Given (A+B)’s one day’s work = 1/12
(B+C)’s one day’s work = 1/15
(C+A)’s one day’s work = 1/20
Adding these three
(A+B) + (B+C) + (C+A) = 2 ( A+B+C)
2 ( A+B+C) ‘s 1 day’s work = 1/12+ 1/15+ 1/20 (take LCM 60)
= (A+B+C) ‘s 1 day’s work = x ½ = 1/10
A, B and C can do the work together in 10 days.
28. A and B can complete a work in 4 days. A alone takes 12 days, in how many days B alone can complete the work?
Answer with Explanation:
Given (A+B)’s one day’s work = 1/4
A’s one day’s work = 1/12
B’s one day’s work= (A+B)’s one day’s work - A’s one day’s work
= ¼ - 1/12 (take LCM 12)
= = 1/6
B alone can complete the work in 6 days.
29. 10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
Answer with Explanation:
Given 10 men and 15 women finish in 6 days
Let 1 man’s one day’s work = x and 1 woman’s one day’s work = y
10x +15y = 1/6 -------------- (1)
But given one alone complete in 100 days
x = 1/100
Substitute x in (1)
10 x 1/100 + 15y = 1/6
1/10 + 15y = 1/6
15y = 1/6 – 1/10 = = = 1/15
y = 1/15 x 1/15 = 1/225
One woman alone finishes the work in 225 days.
30. A and B take 15 and 20 days respectively. They worked for 4 days, and then the fraction of work left was:
Answer with Explanation:
Given A’s one day’s work = 1/15
B’s one day’s work = 1/20
(A + B)’s one day’s work = 1/15 + 1/20 = = 7/60
4 day’s (A+B)’s work = x 4 =
The remaining work = 1 - = =
31. X can do in 40 days. He worked for 8 days and then Y finished it in 16 days. How long together take to finish the work?
Answer with Explanation:
X’s one day’s work = 1/40
8 day’s work = 1/40 x 8 = 1/5
Remaining work = 1-1/5 = 4/5
Now 4/5 work is done by Y in 16 days
Whole work will be done by Y in 16 x 5/4 = 20 days
X’s one day’s work = 1/40; Y’s one day’s work = 1/20
(X+Y)’s one day’s work = 1/40 + 1/20 (take LCM = 40) =
Both together will finish the work in 40/3 days = 13 1/3 days.
32. A does 4/5 of the work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone take to finish the whole work?
Answer with Explanation:
Given 4/5 work done by A in 20 days.
Whole work will be done in 20 x 5/4 = 25 days
Remaining work = 1- 4/5 = 1/5
1/5 work done by (A +B) in 3 days
Whole work will be done in 3 x 5/1 = 15 days
(A+B)’s one day’s work = 1/15
A’s one day’s work = 1/25
B’s one day’s work = 1/15-1/25 = 2/75
B alone to do the work 75/2 days = 37 ½ days.
33. A takes 3 days and B 2 days. Both finished the work and got Rs.150. What is the share of A ?
Answer with Explanation:
Given A’s one day’s work = 1/3
B’s one day’s work = ½
(A + B)’s one day’s work = 1/3 + ½ = 5/6
A’s share is x Amount
x 150
1/3 x 6/5 x 150
60
The share of A is Rs. 60.
34. A can lay railway track between given stations in 16 days and B can do the same job in 12 days. With the help of C, they did the job in 4 days only. Then, C alone can do the job in:
Answer with Explanation:
Given A’s one day’s work = 1/16
B’s one day’s work = 1/12
With the help of C, (A +B+C)’s one day’s work = ¼
Again (A+B)’s one day’s work = 1/16 + 1/12 = 7/48
C’s one day’s work = (A+B+C)’s one day’s – (A+B)’s one day’s work
= ¼ - 7/48 = 5/48
C alone can finish the work is 48/5 = 9 3/5 days.
35. Raju and Enoos are working on an assignment. Raju takes 6 hours to type 32 pages on a computer, while Enoos 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?
Answer with Explanation:
Given Raju takes 6 type 32 pages
1 hours to type = 32/6 = 16/3 page
Again Enoos takes 5 hours to type 40 pages
one hours to type = 40/5 = 8 page
Both together to type in one hour = 16/3 + 8 = 40/3
Ie 40/3 page type in one hour
110 page will be type in 110 x x 1 = 8.25 minutes.
36. A works 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:
Answer with Explanation:
Given A works twice as fast as B
Ie A finish work half of an hour in B.
Given B finish in 12 days
Ie A finishes in 6 days
A’s one day’s work = 1/6
B’s one day’s work = 1/12
(A+B)’s one day’s work = 1/6 + 1/12 = 3/12 = ¼
Both together finish the work in 4 days.
37. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:
Answer with Explanation:
Ratio of times taken by A and B = 125 : 100
= 5 ; 4
Ie 5 : 4 :: 20 : x
5x = 4 x 20
X = 80/5 = 16
X = 16 days.
38. A is 50% as efficient as B. C does half of the work done by A and B together. If C alone does the work in 40 days, then A, B and C together can do the work
Answer with Explanation:
Given C done the work half of (A + B)
C’s one day’s work = --------(1)
But given C alone done the work 1/40
2c is the 1 day’s work of (A+B) [from (1)]
2 x 1/40 is the one day’s work of (A+B)
(A+B)’s one day’s work = 1/20
(A+B+C)’s one day’s work = 1/20 + 1/40 = 3/40
A, B and C together do the work in 40/3 = 13 1/3 days.
39. A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in:
Answer with Explanation:
Given A’s one day’s work = 1/15
B’s one day’s work = 1/10
(A+B)’s one day’s work = 1/15 + 1/10 = 1/6
(A+B)’s 2 day’s work = 1/6 x 2 = 1/3
Remaining (1- 1/3) = 2/3
One work is done by A in 15 days
2/3 work is done by A in 15 x 2/3 = 10 days
The whole work finishing time is 10 + 2 = 12 days.
40. A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 day. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
Answer with Explanation:
Given (A+B)’s one day’s work = 1/30
(B+C)’s one day’s work = 1/24
(C+A)’s one day’s work = 1/20
Adding these three
(A+B) + (B+C) + (C+A) = 2 ( A+B+C)
2 ( A+B+C) ‘s 1 day’s work = 1/30+ 1/24+ 1/20 (take LCM 120)
= (A+B+C) ‘s 1 day’s work = x ½ = 1/16
(A+B+C) ‘s 10 day’s work = 1/16 x 10 =10/16 = 5/8
Remaining work = 1 – 5/8 = 3/8
A alone done the work = (A+B+C) ‘s 1 day’s work - (B+C)’s one day’s work
= 1/16- 1/24 = 1/48
1/48 days are need to finish one work for A
3/8 work done by A in 3/8 x 48/1 x 1 = 18 days.
41. A, B and C are employed to do a piece of work for Rs.529. A and B together are supposed to do of the work and B and C together of the work. What amount should A be paid?
Answer with Explanation:
Given (A+B)’s one day’s work = 19/23
(B+C)’s one day’s work = 8/23
A’s one day’s work = 1- = = 15/23
A’s share amount is Rs. = x 529
Rs. 345/-
42. A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
Answer with Explanation:
Given (A+B)’s one day’s work = 1/12
A’s one day’s work = 1/20
To get B’s one day’s work = (A+B)’s one day’s work - A’s one day’s work
= 1/12 – 1/20 (take LCM = 60)
= = 2/60 = 1/30
But B does the work only ½ a day = 1/30 x 2 = 1/60
(A+B)’s one day’s work = 1/20 + 1/60 = = 1/15
A and B can finish the work together in 15 days.
43. Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and woman?
Answer with Explanation:
Twenty women can do a work in sixteen days = 16/20
Sixteen men can complete the same work in fifteen days = 15/16
The ratio is = 15/16 : 16/20
320 : 240
4 : 3
44. 12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job complete the remaining work, if it is to be completed in 3 days?
Answer with Explanation:
Members Days
Men 12 4
Women 15 4
12 : 15 = 4 : 4
48 = 60
Members Days
Men 6 2
Women x 3
6 : x = 2:3 12 =3x x = 4
Now substitute x value in women whole work = 60/4 = 15 days
