Question 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?

Accepted Answer

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

Question 2

A and B can do a job together in 7 days. A is 1¾ times as efficient as B. The same job can be done by A alone in :

Accepted Answer

(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

Question 3

A can lay 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:

Accepted Answer

(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

Question 4

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 :

Accepted Answer

(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.

Question 5

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?

Accepted Answer

A's 2 day's work = ❨ 1 x 2 ❩ = 1 . 20 10 (A + B + C)'s 1 day's work = ❨ 1 + 1 + 1 ❩ = 6 = 1 . 20 30 60 60 10 Work done in 3 days = ❨ 1 + 1 ❩ = 1 . 10 10 5 Now, 1 work is done in 3 days. 5 ∴ Whole work will be done in (3 x 5) = 15 days.

Question 6

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?

Accepted Answer

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. 8 8

Question 7

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?

Accepted Answer

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.

Question 8

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?

Accepted Answer

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

Question 9

Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar 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?

Accepted Answer

Number of pages typed by Ravi in 1 hour = 32 = 16 . 6 3 Number of pages typed by Kumar in 1 hour = 40 = 8. 5 Number of pages typed by both in 1 hour = ❨ 16 + 8 ❩ = 40 . 3 3 ∴ Time taken by both to type 110 pages = ❨ 110 x 3 ❩ hours 40 = 8 1 hours (or) 8 hours 15 minutes. 4

Question 10

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:

Accepted Answer

(A + B)'s 1 day's work = 1 10 C's 1 day's work = 1 50 (A + B + C)'s 1 day's work = ❨ 1 + 1 ❩ = 6 = 3 . .... (i) 10 50 50 25 A's 1 day's work = (B + C)'s 1 day's work .... (ii) From (i) and (ii), we get: 2 x (A's 1 day's work) = 3 25 ⟹ A's 1 day's work = 3 . 50 ∴ B's 1 day's work ❨ 1 - 3 ❩ = 2 = 1 . 10 50 50 25 So, B alone could do the work in 25 days.

Question 11

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?

Accepted Answer

(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)

Question 12

X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

Accepted Answer

Work done by X in 4 days = ❨ 1 x 4 ❩ = 1 . 20 5 Remaining work = ❨ 1 - 1 ❩ = 4 . 5 5 (X + Y)'s 1 day's work = ❨ 1 + 1 ❩ = 8 = 2 . 20 12 60 15 Now, 2 work is done by X and Y in 1 day. 15 So, 4 work will be done by X and Y in ❨ 15 x 4 ❩ = 6 days. 5 2 5 Hence, total time taken = (6 + 4) days = 10 days.

Question 13

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 :

Accepted Answer

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

Question 14

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?

Accepted Answer

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

Question 15

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:

Accepted Answer

Ratio of times taken by A and B = 1 : 3. The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day. If difference of time is 2 days, B takes 3 days. If difference of time is 60 days, B takes ❨ 3 x 60 ❩ = 90 days. 2 So, A takes 30 days to do the work. A's 1 day's work = 1 30 B's 1 day's work = 1 90 (A + B)'s 1 day's work = ❨ 1 + 1 ❩ = 4 = 2 30 90 90 45 ∴ A and B together can do the work in 45 = 22 1 days. 2 2

Question 16

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 :

Accepted Answer

(A + B + C)'s 1 day's work = 1 ; 6 (A + B)'s 1 day's work = 1 ; 8 (B + C)'s 1 day's work = 1 . 12 ∴ (A + C)'s 1 day's work = ❨ 2 x 1 ❩ - ❨ 1 + 1 ❩ 6 8 12 = ❨ 1 - 5 ❩ 3 24 = 3 24 = 1 . 8 So, A and C together will do the work in 8 days.

Question 17

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 m…

Accepted Answer

(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.

Question 18

10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

Accepted Answer

1 woman's 1 day's work = 1 70 1 child's 1 day's work = 1 140 (5 women + 10 children)'s day's work = ❨ 5 + 10 ❩ = ❨ 1 + 1 ❩ = 1 70 140 14 14 7 ∴ 5 women and 10 children will complete the work in 7 days.

Question 19

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 :

Accepted Answer

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.

Question 20

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:

Accepted Answer

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.

Time and Work Questions