Time and Work questions

CONCEPT TEST: Time & Work

1. A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
A.
 1 4
B.
 1 10
C.
 7 15
D.
 8 15

 A’s 1 day’s work = 1 ; 15

 B’s 1 day’s work = 1 ; 20

 (A + B)’s 1 day’s work = 1 + 1 = 7 . 15 20 60

 (A + B)’s 4 day’s work = 7 x 4 = 7 . 60 15

 Therefore, Remaining work = 1 – 7 = 8 . 15 15

1. A can laid railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
A.
 9 1 days 5
B.
 9 2 days 5
C.
 9 3 days 5
D. 10

 (A + B + C)’s 1 day’s work = 1 , 4

 A’s 1 day’s work = 1 , 16

 B’s 1 day’s work = 1 . 12

 C’s 1 day’s work = 1 – 1 + 1 = 1 – 7 = 5 . 4 16 12 4 48 48

 So, C alone can do the work in 48 = 9 3 days. 5 5
1.  A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
 A. 12 days B. 15 days C. 16 days D. 18    ays
1. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
 A. Rs. 375 B. Rs. 400 C. Rs. 600 D. Rs. 800

Explanation:

 C’s 1 day’s work = 1 – 1 + 1 = 1 – 7 = 1 . 3 6 8 3 24 24

 A’s wages : B’s wages : C’s wages = 1 : 1 : 1 = 4 : 3 : 1. 6 8 24

 C’s share (for 3 days) = Rs. 3 x 1 x 3200 = Rs. 400. 24
1. A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
A. 20 days B.
 22 1 days 2
C. 25 days D. 30 days
1. If 6 men and 8 boys can do a piece of work in 10 days while 26 men 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:
 A. 4 days B. 5 days C. 6 days D. 7 days

Explanation:

Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y.

 Then, 6x + 8y = 1 and 26x + 48y = 1 . 10 2

 Solving these two equations, we get : x = 1 and y = 1 . 100 200

 (15 men + 20 boy)’s 1 day’s work = 15 + 20 = 1 . 100 200 4

15 men and 20 boys can do the work in 4 days.

1. A does 80% 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. 23 days B. 37 days C. 37 D. 40 days

Explanation:

 Whole work is done by A in 20 x 5 = 25 days. 4

 Now, 1 – 4 i.e., 1 work is done by A and B in 3 days. 5 5

Whole work will be done by A and B in (3 x 5) = 15 days.

 A’s 1 day’s work = 1 , (A + B)’s 1 day’s work = 1 . 25 15

 B’s 1 day’s work = 1 – 1 = 4 = 2 . 15 25 150 75

 So, B alone would do the work in 75 = 37 1 days. 2 2
1. A machine P can print one lakh books in 8 hours; machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished?
 A. 11:30 A.M. B. 12 noon C. 12:30 P.M. D. 1:00 P.M.

Explanation:

 (P + Q + R)’s 1 hour’s work = 1 + 1 + 1 = 37 . 8 10 12 120

 Work done by P, Q and R in 2 hours = 37 x 2 = 37 . 120 60

 Remaining work = 1 – 37 = 23 . 60 60

 (Q + R)’s 1 hour’s work = 1 + 1 = 11 . 10 12 60

 Now, 11 work is done by Q and R in 1 hour. 60

 So, 23 work will be done by Q and R in 60 x 23 = 23 hours  2 hours. 60 11 60 11

So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.

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?
 A. 35 B. 40 C. 45 D. 50
Answer: Option BExplanation:Let 1 man’s 1 day’s work = x and 1 woman’s 1 day’s work = y.

 Then, 4x + 6y = 1 and 3x + 7y = 1 . 8 10

 Solving the two equations, we get: x = 11 , y = 1 400 400

 1 woman’s 1 day’s work = 1 . 400

 10 women’s 1 day’s work = 1 x 10 = 1 . 400 40

Hence, 10 women will complete the work in 40 days.

1. 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 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
 A. 18 days B. 24 days C. 30 days D. 36 days

Explanation:

 2(A + B + C)’s 1 day’s work = 1 + 1 + 1 = 15 = 1 . 30 24 20 120 8

 Therefore, (A + B + C)’s 1 day’s work = 1 = 1 . 2 x 8 16

 Work done by A, B, C in 10 days = 10 = 5 . 16 8

 Remaining work = 1 – 5 = 3 . 8 8

 A’s 1 day’s work = 1 – 1 = 1 . 16 24 48

 Now, 1 work is done by A in 1 day. 48

 So, 3 work will be done by A in 48 x 3 = 18 days.
1. 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 in :
 A. 4 days B. 6 days C. 8 days D. 18 days

Explanation:

Ratio of rates of working of A and B = 2 : 1.

So, ratio of times taken = 1 : 2.

 B’s 1 day’s work = 1 . 12

 A’s 1 day’s work = 1 ; (2 times of B’s work) 6

 (A + B)’s 1 day’s work = 1 + 1 = 3 = 1 . 6 12 12 4

So, A and B together can finish the work in 4 days.

1. 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 :
 A. 8 days B. 10 days C. 12 days D. 15    Days

Explanation:

 (A + B)’s 1 day’s work = 1 + 1 = 1 . 15 10 6

 Work done by A and B in 2 days = 1 x 2 = 1 . 6 3

 Remaining work = 1 – 1 = 2 . 3 3

 Now, 1 work is done by A in 1 day. 15

 2 work will be done by a in 15 x 2 = 10 days. 3 3

Hence, the total time taken = (10 + 2) = 12 days.

1. 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 a woman?
 A. 3 : 4 B. 4 : 3 C. 5 : 3 D. Data inadequate

Explanation:

(20 x 16) women can complete the work in 1 day.

 1 woman’s 1 day’s work = 1 . 320

(16 x 15) men can complete the work in 1 day.

 1 man’s 1 day’s work = 1 240

So, required ratio
 = 1 : 1 240 320
 = 1 : 1 3 4
= 4 : 3 (cross multiplied)

1. A and B can do a job together in 7 days. A is 1 times as efficient as B. The same job can be done by A alone in :
A.
 9 1 days 3
B. 11 days
C.
 12 1 days 4
D.
 16 1 days 3

Explanation:

 (A’s 1 day’s work) : (B’s 1 day’s work) = 7 : 1   =   7 : 4. 4

Let A’s and B’s 1 day’s work be 7x and 4x respectively.

 Then, 7x + 4x = 1 11x = 1 x = 1 . 7 7 77

 A’s 1 day’s work = 1 x 7 = 1 . 77 11
1. P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?
A.
 5 5 11
B.
 5 6 11
C.
 6 5 11
D.
 6 6 11

Explanation:

P can complete the work in (12 x 8) hrs. = 96 hrs.

Q can complete the work in (8 x 10) hrs. = 80 hrs.

 P’s1 hour’s work = 1 and Q’s 1 hour’s work = 1 . 96 80

 (P + Q)’s 1 hour’s work = 1 + 1 = 11 . 96 80 480

 So, both P and Q will finish the work in 480 hrs. 11

 Number of days of 8 hours each = 480 x 1 = 60 days = 5 5 days. 11 8 11 11

1. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:
 A. 4 days B. 6 days C. 8 days D. 12 days

Explanation:

 Suppose A, B and C take x, x and x days respectively to finish the work. 2 3

 Then, 1 + 2 + 3 = 1 x x x 2

 6 = 1 x 2

x = 12.

So, B takes (12/2) = 6 days to finish the work.

1. A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:
 A. 15 days B. 20 days C. 25 days D. 30 days

Explanation:

 A’s 1 hour’s work = 1 ; 4

 (B + C)’s 1 hour’s work = 1 ; 3

 (A + C)’s 1 hour’s work = 1 . 2

 (A + B + C)’s 1 hour’s work = 1 + 1 = 7 . 4 3 12

 B’s 1 hour’s work = 7 – 1 = 1 . 12 2 12

B alone will take 12 hours to do the work.

1. 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 :
 A. 8 days B. 10 days C. 12 days D. 15 days

Explanation:

 (A + B)’s 1 day’s work = 1 + 1 = 1 . 15 10 6

 Work done by A and B in 2 days = 1 x 2 = 1 . 6 3

 Remaining work = 1 – 1 = 2 . 3 3

 Now, 1 work is done by A in 1 day. 15

 2 work will be done by a in 15 x 2 = 10 days. 3 3

Hence, the total time taken = (10 + 2) = 12 days.

1. 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 forced to leave after 3 days. The remaining work was done by A in:
A. 5 days B. 6 days
C. 10 days D.
 10 1 days 2

Explanation:

 (B + C)’s 1 day’s work = 1 + 1 = 7 . 9 12 36

 Work done by B and C in 3 days = 7 x 3 = 7 . 36 12

 Remaining work = 1 – 7 = 5 . 12 12

 Now, 1 work is done by A in 1 day. 24

 So, 5 work is done by A in 24 x 5 = 10 days.
1. X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?
A.
 13 1 days 3
B. 15 days
C. 20 days D. 26 days

Explanation:

 Work done by X in 8 days = 1 x 8 = 1 . 40 5

 Remaining work = 1 – 1 = 4 . 5 5

 Now, 4 work is done by Y in 16 days. 5

 Whole work will be done by Y in 16 x 5 = 20 days. 4

 X’s 1 day’s work = 1 , Y’s 1 day’s work = 1 . 40 20

 (X + Y)’s 1 day’s work = 1 + 1 = 3 . 40 20 40

 Hence, X and Y will together complete the work in 40 = 13 1 days. 3 3