Question 1

A and B can complete a work in 12 days and 18 days, respectively. A begins to do the work and they work alternately one at a time for 1 days each. The whole work will be completed in how many days?

Accepted Answer

(A + B)'s 2 day's work = (1/12) + (1/18) = 5/36 (A + B)'s 14 day's work = (5/36) x 7 = 35/36 Remaining work = 1 - (35/36) = 1/36 Now, it is the turn of A . A's 1 day's work = 1/12 ∴ 1/36 work is done by A in 12 x (1/36) days = 1/3 days ∴ Total time taken = 141/3 days

Question 2

A can build up a structure in 8 days and B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of structure?

Accepted Answer

A,s 1 days work =1/8 B's 1 day's work in breaking the building = 1/3 Now, according to the question, A's 4 day's work = 4 x (1/8) = 1/2 Now, A's and B's 2 day's work = 2[(1/8) - (1/3)] = 2 x (-5/24) = -10/24 Total work done in 6 days = 1/2 + (-10/24) = (12 - 10)/24 = 2/24 = 1/12 Remaining work = 1 - (1/12) = 11/12 Now, A has complete the work, so A can complete in N days. (1/8) x N = 11/12 ⇒ N = (11 x 8) / 12 N = (11 x 2)/3 = 71/3 days

Question 3

Mr. Prashant has to build a wall 1000 meters long in 50 days. He employs 56 men but at the end of 27 days finds that only 448 meters are built. How many men must be employed so that the work may be finished in time?

Accepted Answer

Y = 56 x (27/23) x (552/448) =81 Extra men required =81-56 =25

Question 4

Mr. Modi can copy 40 pages in 10 minutes, Mr. Xerox and Mr. Modi both working together can copy 250 In 25 minutes. In how many minutes Mr. Xerox can copy 36 pages?

Accepted Answer

Efficiency ( per minute) of Modi = 4 copies/min Efficiency of Modi and Xerox together = 10 pages/min ∴ Efficiency of Xerox alone = 10 - 4 = 6 pages/min ∴ Mr. Xerox needs 6 min to copy 36 pages.

Question 5

25 men and 15 women can complete a piece of work in 12 days. All of them start working together and after working for 8 days the women stopped working. 25 men complete the remaining work in 6 days. how many days will it take for completing the entir…

Accepted Answer

25 men and 15 women can complete, a piece of work in 12 days. ∴ Work done by them in 8 days = 8/12 = 2/3 Remaining work is completed by 25 men in 6 days ∴ Time taken by 25 men to complete the whole work = 3 x 6 = 18 days From the question Time taken by 15 women to complete the whole work = 1 / (1/12 - 1/18) = 1 / {(3 - 2) / 36} = 36/(3 - 2) = 36 days

Question 6

A can do a piece of work in 12 days, B can do the same work in 8 days and c can do the same job in 4 / 5 th time required by both A and B. A and B work together for 3 days, then C complete days did C work?

Accepted Answer

As per question, work of A for 1 day = 1/12 and work of B for 1 day = 1/8 ∴ Work of (A + B) together for 1 day = 1/12 + 1/8 = (2 + 3)/24 = 5/24 ⇒ Work of (A + B) together for 3 days = 3 x (5/24) = 5/8 ⇒ Remaining work after 3 days = 1 - 5/8 = 3/8 ∵ C can do the same work in = 4/5th time required by (A + B) = 4/5 x 24/5 = 96/25 days ⇒ Work of C for 1 day = 25/96 part. ⇒ 25/96 part work can be done by C in 1 day ⇒ 3/8 part work can be done by C in = 96/25 x 3/8 days = 36/25 days = 111/25 ∴ The complete day C did the work = 1 day.

Question 7

A completes a work in 15 days. B complete the same work in 20 days. A started working alone after 1 days B joined him. How many day will they now take together to complete the remaining work?

Accepted Answer

Work of A for 1 day = 1/15 Work of B for 1 day = 1/20 Work of (A + B) together for 1 day = 1/15 + 1/20 = (4 + 3)/60 = 7/60 Remaining work after A alone does for 1 day = 1 - 1/15 = 14/15 ∵ 7/60 part-work can be complete by (A + B) in 1 days ∴ 14/15 part-work can be completed by (A + B) in = (60/7) x (14/15) = 8 days.

Question 8

A can do a piece of work in 10 days and B can do the same piece of work in 20 days. They start the work together but after 5 days A leaves off, B will do the remaining piece of work in?

Accepted Answer

(A + B)'s 5 day's work = 5 x (1/10 + 1/20) = 3/4 Remaining work = (1 - 3/4) = 1/4 1/20 work is done by B in = 1 day ∴ 1/4 work is done by B in = 20 x (1/4) i.e., 5 days.

Question 9

Twelve men can complete a work in 8 days. Three days after they started the work, 3 more men joined them. In how, many days will all of them together complete the remaining work

Accepted Answer

1 men's one day's work = 1/96 12 men's 3 day's work = 3 x (1/8) = 3/8 Remaining work = (1 - 3/8) = 5/8 15 men's 1 day's work = 15/96 Now, 15/96 work is done by them in 1 day ∴ 5/8 work will be done by them in = (96/15) x (5/ 8) i.e., 4 days

Question 10

A can complete a job in 9 days, B in 10 days and C in 15 days. B and C start the work and are forced to leave after 2 days. The time taken to complete the remaining work is?

Accepted Answer

(B + C)'s 2 day's work = 2 x (1/10 + 1/15) = 1/3 Remaining work = (1 - 1/3) = 2/3 ∵ 1/9 work is done by A in 1 day ∴ 2/3 work is done by A in (9 x 2) / 3 = 6 days

Question 11

Twenty-four men can complete a work in sixteen days. Thirty-two women can complete the same work in twenty-four days. Sixteen men and Sixteen women started working and worked for twelve days. How many more men are to be added to complete the remaini…

Accepted Answer

24 men complete the work in 16 days ⇒ Work that 16 men complete in 12 days = (16/24) x (12/ 16) = 1/2 part of work in 12 days. 32 women complete the work in 24 days ∴ Work that 16 women complete in 14 days = (16/32) x (14/24) = 7/24 part of work in (12 + 2) = 14 days. So, the remaining part of the work which done by (sixteen men + sixteen women) and required additional no. of men in 2 days = 1 - (1/2 + 7/24) = 1/2 - 7/24 = 5/24 (part) Now, in 2 days 5/24 part part of the work is done by (24 x 16)/ 2 x (5/ 24) = 40 men ∴ Required additional no. of men = 40 - 16 =24.

Question 12

Typist A can type a report in 16 hours. Typist B can type the same report in 20 hours and the typist C in 24 hours. All the three typist started typing at 9.00 a.m. at 1.00 p.m. the typist A stopped typing. The other two typists finished the job. Ap…

Accepted Answer

Work of (A + B + C) for 1 hour = 1/16 + 1/20 + 1/24 = 37/240 ∴ Work of (A + B + C) for 4 hours = 4 x 37/240 = 37/60 ∴ Remaining work = 1 - 37/60 = 23/60 ∴ Work of (B + C) for 1 hour = 1/20 + 1/24 = 11/120 ∵ 11/120 work is done by (B + C) in 1 hour ∴ 23/60 work is done by (B + C) = 120/11 x 23/60 = 46/11 hours = 4 hours 11 min. ∴ The type at which the report was typed = 01 : 00 + 04 : 11 = 05 : 11 p.m.

Question 13

14 persons can complete a work in 16 days. 8 persons started the work 12 days after they started the work 8 more person joined them. How many days will they take to complete the remaining work?

Accepted Answer

∵ 14 person complete in 16 days = 1 work ∴ 8 person complete in 12 days = 1 x (8/14) x (12/16) = 3/7 ∴ Remaining work = 1 - 3/7 = 4/7 and total number of person = 8 + 8 = 16 ∴ 14 person do 1 work in 16 days ∴ 16 person do 4/7 work in 16 x (14/16) x (4/7) = 8 days

Question 14

If 5 men and 3 boys can reap 23 hectares in 4 days and if 3 men and two boys can reap 7 hectares in 2 days. How many boys must assist 7 men in order that they may reap 45 hectares in 6 days?

Accepted Answer

5 men + 3 boys can reap 23 hectares in 4 days ......(i) 3 men + 2 boys can reap 7 hectares in 2 days ......(ii) ∴ From (i), 14( 5 men + 3 boys) can reap 23 x 14 hectares in 4 days Now, from (ii) ⇒ 23 (3 men + 2 boys) can reap 7 x 2 x 23 hectares in 4 days ∵ 14(5 men + 3 boys) = 23 (3 men + 2 boys) ⇒ 70 men + 42 boys = 69 men + 46 boys ∴ 1 men = 4 boys Now, 5 men + 3 boys = 23 boys ⇒ 23 boys can reap 23 hectare 4 days ⇒ 1 boy can reap 1 hectares in 4 days ⇒ 4 boys can reap 1 hectare in 1 day ⇒ 4 x 45 boys can reap 45 hectaes in 1 day ⇒ 4 x 45 / 6 boys can reap 45 hectares in 6 days ∴ 30 boys can reap 45 hectares in 6 days But 30 boys = 28 boys + 2 boys = 7 men + 2 boys Hence, 2 boys can assist 7 men for the work.

Question 15

A piece of work was to be completed in 40 days, a number of men employed upon it did only half the work in 24 days, 16 more men were then set on and the work was completed in the specified time, how many men were employed at first?

Accepted Answer

Let N men were employed at first ∵ N men do 1/2 of the work in 24 days ∴ 1 man do the whole work in 24 x 2 x N = 48N days Now, from the question, (N + 16) men do the remaining work (1 - 1/2) = 1/2 in (40 - 24) = 16 days ∴ 1 man do the whole work in 16 x 2 x (N + 16) days ∴ 48N = 32(N + 16) ∴ N = 32 men

Question 16

A can do a piece of work in 10 days. B can do it in 24 days. If C also works with them then it take only 6 days to complete the whole work. In how many days C alone can complete the whole work?

Accepted Answer

Efficiency of A = 100/10 = 10% Efficiency of B = 100/24 = 4.16% Efficiency of (A+B+C) = 100/6 = 16.66% Efficiency of C = (16.66) - (10 + 4.16) = 2.5% Number of days required by C alone to finish the work = 100/2.5 = 40 days

Question 17

If 15 men can prepare 12 toys working 5 h per day in 16 days, then in how many days can 10 men prepare 15 toys working 8 h per day?

Accepted Answer

Using formula M1D1T1W1 = M2D2T2W2 M1 = 15, M2 = 10, D1 = 16, D2 = ? T1 = 5, T2 = 8, W1 = 15, W2 = 12 Now, 15 x 16 x 5 x 15 = 10 x D2 x 8 x 12 D2 = (15 x 16 x 5 x 15)/(10 x 8 x 12) = (15 x 15)/12 = 75/4 = 183/4 days

Question 18

In a garrison, there was food for 1000 soldiers for one month. After 10 days, 1000 more soldiers joined the garrison. How long would the soldiers be able to carry on with the remaining food?

Accepted Answer

Let us assume that each soldiers eats one unit of food per day. Thus, total units of food at the beginning will be 1000 x 30 = 30000. After 10 days the 100 soldiers would have eaten 1000 x 10 = 10000 units of food. Thus, food left after 10 days equals 20000 units. Now, there are a total of 2000 soldiers who eat one unit of food everyday. Now, 30 x 1000 = 1000 x 10 + 2000 x D (here, D is number of days food will last) ⇒ 30000 - 10000 = 2000 x D ∴ D = 20000/2000 = 10 days

Question 19

A and B can do a piece of work separately in 8 and 12 h. If they work alternate hours, A starting, when will the work be finished?

Accepted Answer

(A + B +)'s 2 h work = 1/8 + 1/12 = 5/24 (A + B)'s 8 h work = (5 x 8)/(24 x 2) = 5/6 Work done by A in 9th h = 1/8 Total work done upto 9th h = 5/6 + 1/8 = 23/24 Remaining wok = 1/24 B's 1 h work = 1/12 B can do 1/24 of the work = (1/24) x 12 = 1/2 h So, both can finish the job in 91/2 h.

Question 20

A contractor undertook to do a piece of work in 9 days. He employed a certain number of laborious but 6 of them being absent from the very first day, the rest could finish the work in 15 days. Find the number of men originally employed.

Accepted Answer

Let the number of men originally employed = x So, (x - 6) men could finish the work in 15 days and x men could finish the work in 9 days. ∴ 9x = 15(x - 6) ⇒ x = 15

Time and Work Questions