Time and Work.44

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? Ans 17 1/7

Difficulty Level : Easy Moderately easy Difficult

Basic Formula:

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

Time and Work, BU www.aptitudecoach.com

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 ans 84 days


Basic Formula:

Subtraction of fraction

- =


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

= - (take LCM)

= = = 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 ? ans 3 days


Basic Formula:

Addition and multiplication of fraction


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

ans : 7 1/ 2 days


Basic Formula:

Subtraction of fraction


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 ans 9 3/8


Basic Formula:

Addition with fraction


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 : ans 30 days


Basic Formula:

Addition and subtraction of fractions


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


= = = 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 ans : 60 days


Basic Formula:

Fraction’s Subtraction


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 ans: 9


Basic Formula:

Fraction’s addition and subtraction



B’s one day’s work = 1/40


= =

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 ?ans 30

days


Basic Formula:

Fraction’s addition with variable


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 ans 7 ½


Basic Formula:

Ratio multiplication A:b:: c:dAd = bc


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 ans 16 2/3


Basic Formula:

Fraction’s addition


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. Ans: 21 days


Basic Formula:

Ratio comparison

A:b:: c:dAd = bc


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 : ans 15 days


Basic Formula:

Fraction’s Multiplication


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 ans 10 1/5


Basic Formula:

Fraction’s addition, subtraction, multiplication





= =

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? ans 3 days


Basic Formula:



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 ? ans 120 days


Basic Formula:



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 : ans 9 days


Basic Formula:

Fraction’s addition and multiplication


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 : 16


Basic Formula:






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 ans 45


Basic Formula:

Fraction’s multiplication


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? Ans 6


Basic Formula:

Fractions multiplication and subtraction


(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? Ans 9


Basic Formula:

Fractions multi0plication and subtraction


(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 ans 4


Basic Formula:

Fraction’s subtraction and multiplication


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?

Ans 9


Basic Formula:

Ratio comparison


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 : 17 1/7


Basic Formula:

Fraction’s Addition


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 : A


Basic Formula:






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 : 8 days


Basic Formula:

Fraction’s subtraction and addition




(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 : 10 days


Basic Formula:






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: 6


Basic Formula:

Fraction’s subtraction




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 : 225


Basic Formula:



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 : 8/15


Basic Formula:

Fraction’s subtraction and addition


Given A’s one day’s work = 1/15


(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 : 13 1/3


Basic Formula:

Fraction’s addition, multiplication


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: 37 ½


Basic Formula:

Fraction’s multiplication and subtraction


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


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 : 60


Basic Formula:

Fraction’s Multiplication



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 :

a. days b. days c. days d. 10 days


Basic Formula:





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. Ronald and Elan are working on an assignment. Ronald takes 6 hours to type

32 pages on a computer, while Elan 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?

a. 7 hours 30 minutes b. 8 hours

c. 8 hours 15 minutes d. 8 hours 25 minutes


Basic Formula:

Fractions Multiplication


Given Ronald takes 6 type 32 pages

1 hours to type = 32/6 = 16/3 page

Again Elan 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:

a. 4 days b. 6 days c. 8 days d. 18 days


Basic Formula:



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+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:

a. 15 b. 16 c. 18 d. 25


Basic Formula:

Ratio comparison

A:b:: c:dAd = bc


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 in:

a. days b. 15 days c. 20 days d. 30 days


Basic Formula:

Fractions addition


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:



Basic Formula:

Fraction’s addition, multiplication and subtraction




(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?



Basic Formula:

Fraction’s addition, multiplication and subtraction





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?

a. Rs.315 b. Rs.345 c. Rs.355 d. Rs.375


Basic Formula:

Fraction’s subtraction and Multiplication




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?

a. 10 days b. 11 day c. 15 days d. 20 days


Basic Formula:

Fractions Addition and Subtraction




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?

a. 3 : 4 b. 4 : 3 c. 5 : 3 d. Data inadequate


Basic Formula:

Ratio


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?

a. 15 b. 18 c. 22 d. None of these


Basic Formula:

Ratio comparison


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


Time and Work.44

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Transcript of Time and Work.44