Question 1

16 men and 12 women together complete a work in 20 days. If 18 women complete the same work in 40 days. Then how many days will be taken by 12 men and 27 women together to complete the same work?

Accepted Answer

∵ In 20 days the work is completed by = 16 men + 12 women ∴ In 1 day the work is completed by = 20 x (16 men + 12 women ) = 320 men + 240 women In 40 days the work is complete by 18 women ∴ 1 day the work is complete by = 18 x 40 = 720 women ∵ 720 women = 320 men + 240 women ⇒ (720 - 240)women = 320 men ⇒ 480 women = 320 men ∴ 1 men = 480/320 = 3/2 women ∴ 12 men + 27 women = 12 x (3/2) + 27 = 45 women ∵ 18 women complete work in 40 days ∴ 45 women complete 1 work = 40 x 18/45 = 16 days

Question 2

A report of 100 pages is to be typed by three typists. Typist A can type 100 pages in 10 hours. Typist B can type the same pages in 20 hours and typist C in 25 hours. Allthe three typist started typing at 09.00 a.m. At 01.00 p.m. typist A stopped ty…

Accepted Answer

∵ No. of pages typed by the typist A in 4 hours = 100 x 4/10 = 40 ∴ No. of remaining pages = 100 - 40 = 60 Let B and C worked for H hours ∵ (100 x H)/20 + (100 x H)/25 = 60 ⇒ 5H + 4H = 60 ∴ H = 60/9 = 20/3 hours = 6 hours 40 min ∴ The time at which the report was typed 03.40 p.m.

Question 3

15 men can complete a work in 10 days while 20 boys can complete the same work in 15 days. How many days will 10 men and 10 boys together take to complete the same work?

Accepted Answer

∵ In 10 days a work is complete by 15 men ∴ In 1 day a work is complete by = 15 x 10 = 150 men ∵ In 5 days the work is complete by = 20 boys ∴ 1 day the work is completed = 20 x 15 = 300 boys ⇒ 150 men = 300 boys or 1 men = 300/150 = 2 boys 10 men = 2 x 10 = 20 boys 10 men + 10 boys = 20 + 10 = 30 boys ∵ 20 boys complete the work in 15 days ∴ 30 boys complete the work in (15 x 20)/30 = 10 days

Question 4

Ganesh, Ram and Sohan together can do a work in 16 days. If Ganesh and Ram together can do the same work in 24 days then, how long will take Sohan alone to do the same work?

Accepted Answer

∵ Work of (Ganesh, Ram and Sohan) for 1 day = 1/16 and work of Ganesh and Ram for 1 day = 1/24 ⇒ Work of Sohan for 1 day = 1/16 - 1/24 = 1/48 ∴ Sohan alone will complete the work in = 1/(1/48) days = 48 days.

Question 5

A and B can complete a work in 8 days. working together. B alone can do it in 12 days. After working for 4 days, B left the work. How many days will A take to complete the remaining work?

Accepted Answer

( A + B) 's 1 days work = 1/8 B's 1 days work = 1/12 ∴ A's 1 day's work = (1/8) - (1/12) = (3 - 2)/24 = 1/24 ∴ A can complete the work in 24 days Now, B's 4 days work = 4/12 = 1/3 Remaining work = 1 - 1/3 = 2/3 As, time taken by A to complete the work is 24 days. ∴ Time taken by A to do 2/3 of the work = 2/3 x 24 = 16 days

Question 6

Ajay can do a piece of work in 25 days and Sanjay can finish it in 20 days. They work together for 5 days and then Ajay goes away. In how many days will Sanjay finish the remaining work?

Accepted Answer

Ajay' s 1 days work = 1/25 Similarly, sanjay's 1 days work = 1/20 Ajays and Sanjay 's together 1 day's work = (1/25) + (1/20) = (4 + 5)/100 = 9/100 Their 5 day's work together = 5 x 1 day's work = 5 x (9/100) = 45/100 Remaining work = 1 - (5/100) = 55/100 Now, this remaining work is done by Sanjay. Let Sanjay takes N days to complete it. Then, (1/20) x N = 55/100 ⇒ N = (55 x 20)/100 ∴ N = 11 days So, remaining work is done in 11 days by Sanjay.

Question 7

A and B together can complete a work in 3 days. They started together but after 2 days, B left the work. If the work is completed after 2 more days, B alone could do the work in how many days?

Accepted Answer

(A + B)'s 2 day's work = 2 x (1/3) = 2/3 Remaining work = 1 - (2/3) = 1/3 A will complete 1/3 work in 2 A will complete 1 work in 6 A's 1 days work = 1/6 B's 1 day's work = (1/3) - (1/6) = 1/6 ∴ B will take 6 days to complete the work alone.

Question 8

A and B can complete a job in the 24 days working together. A alone can complete it in 32 days. Both of them worked together for 8 days and then A left. The number of days B will take to complete the remaining job is

Accepted Answer

Let B will take N days to complete the remaining job. According to the question (1/A) + (1/B) = 1/24 and 1/A = 1/32 ∴ 1/B = (1/24) - (1/32) = 1/96 ⇒ B = 96 days According to the question, 8[(1/A) + (1/B)] + N x (1/B) = 1 ⇒ 8 x (1/24) + (N/96) = 1 ⇒ (1/3) + (N/96) = 1 ⇒ N/96 = 1 -1/3 ∴ N = (2 x 96)/3 = 64 Hence, B complete the remaining job in 64 days

Question 9

20 workers working for 5 h per day complete a work in 10 days. If 25 workers are employed to work 10 h per days, what is the time required to complete the work?

Accepted Answer

Given, M1= 20, M2 = 25, T1 = 5, T2 = 10, D1 = 10 and D2 = ? According to the formula, M1T1D1= M2T2D2 ⇒ 20 x 5 x 10 = 25 x 10 x D2 ∴ D2 = 20 x 5 x 10/25 x 10 = 4 days

Question 10

90 men are engaged to do piece of work in 40 days but it is found that in 25 days, 2/3 work is complete. How many men should be allowed to go off, so that the work finished in time?

Accepted Answer

Let N men are allowed to go off, M1= 90, D1 = 25, D2 = 15 W1 = 2/3, W2 = 1 - (2/3) = 1/3 M2 = 90 - N According to the formula, M1D1W2 = M2D2W1 ⇒ (90 x 25) (1/3) = (90 - N) x 15 x (2/3) ⇒ 90 x 25 x (1/3) = 10(90 - N) ⇒ 75 = 90 - N ∴ N = 90 - 75 = 15

Question 11

A, Band C can do a piece of work individually in 8, 12 and 15 days, respectively. A and B start working but A quits after working for 2 days. After this, C joins B till the completion of work. In how many days will the work be completed?

Accepted Answer

Work done by A and B in 1 day = (1/8) + (1/12) = 5/24 2 day's work of A and B = 10/24 After 2 day's A left the work ∴ Remaining work = 1 - (10/24) = 14/24 One day work of B and C together = (1/12) + (1/15) = 9/60 So, the number of days required by B and C to finish work = (14/24) / (9/60) = (14/24) x (60/9) = 35/9 ∴ Total days to complete the work = 2 + (35/9) = 53/9 = 58/9 days

Question 12

A and B can do a piece of work in 9 days and 18 days, respectively. As they were ill, they could do 90% and 72% of their efficiency, respectively. How many days will they take to complete the work together?

Accepted Answer

Because of illness, A's 1 day's work = 90% of 1/9 = 1/10 B's 1 day's work = 72% of 1/18 = 1/25 ∴ (A + B)'s 1 day's work = (1/10) + (1/25) = (5 + 2)/50 = 7/50 Hence, time taken by them to complete the work = 50/7 days = 71/7

Question 13

36 workmen are employed to finish a certain work in 48 days. But it is found that in 24 days only 2/5 work is done. How many more men must be employed to finish the work in this?

Accepted Answer

Let N men are employed. Given, M1 = 36, M2 = 36 + N, D1 = 24, D2 = 24, W1 = 2/5, W2 = 1 - 2/5 = 3/5 According to the formula M1D1W2 = M2D2W1 ⇒ 36 x 24 x (3/5) = (36 + N) x 24 x (2/5) ⇒ 36 x 3 = 2(36 + N) ⇒ 108 = 72 + 2N ∴ N = 36/2 = 18 men

Question 14

It is given that 16 men working 18 h a day can build a wall 36 m long, 4 m broad and 24 m high in 20 days. How many men will be required to build a wall 64 m long, 6 m broad and 18 m high working 12 h a day in 16 days?

Accepted Answer

Given, M1 = 16, T1 = 18, W1 = 36 x 4 x 24, D1 = 20 and M2 = ? T2 = 12, W2 = 64 x 6 x 18, D2 = 16 According to the formula, M1D1T1/ W1 = M2D2T2/ W2 ⇒ 16 x 20 x (18/36) x 4 x 24 = M2 x 12 x (16/64) x 6 x 18 ⇒ (15/36) x 24 = M2 x (2/64) x 6 x 18 ∴ M2 = 60 men

Question 15

A men can do a piece of work in 5 days. With the help of his friend, he can do the same work in 3 days. In how many days can his friend complete the work?

Accepted Answer

(Man and his friend)'s 1 day's work = 1/3 Men's 1 day's work = 1/5 His friend's 1 day's work is = 1/3 - 1/5 = 2/15 Hence, his friend can complete the work in 15/2 = 71/2

Question 16

A and B each working alone can do a work in 15 days and 25 days, respectively. They started the work together but B left after some time and A finished the remaining work in 7 days. After how many days from the start did B leave?

Accepted Answer

Let B left work after N days from the start. According to the question, N/25 + (N + 7)/15 = 1 ⇒ (3N + 5N + 35) / 75 = 1 ⇒ 8N = 75 - 35 ⇒ N = 40/8 ∴ N = 5

Question 17

A can complete a work in 20 days and B in 30 days. A worked alone for 4 days and then B complete the remaining work alone with C in 18 days. In how many days can C working alone complete the work?

Accepted Answer

Work done by A in 4 days = 4/20 = 1/5 ∴ Remaining work = 1 - 1/5 = 4/5 Let C can working alone complete the work in N days . According to the question, 18/30 + 18/N = 4/5 ⇒ 18(N + 30) x 5 = 4 x 30 x N ⇒ 90N + 2700 = 120N ⇒ 30N = 2700 ∴ N = 90 days

Question 18

6 men can do a piece of work in 12 days while 8 women can do the same work in 18 days. The same work can be done by 18 children in 10 days. 4 men 12 women and 20 children work together for 2 days. If only men have to complete remaining work in 1 day…

Accepted Answer

6 x 12 men = 8 x 18 women = 18 x 10 children ⇒ 12 men = 24 women = 30 children ⇒ 2 men = 4 women = 5 children Now, 4 men + 12 women + 20 children = 4 men + 6 men + 8 men = 18 men Time to do remaining work in 1 man = (6 x 12 - 18 x 2) = 36 days ∴ Required number of men to finish the work in 1 days = 36

Question 19

A, B and C can do a piece of work in 18, 24 and 36 days, respectively. They work alternately, first day C, second day B and third day A, fourth day C and so on. How many days will be needed to complete the work like this way?

Accepted Answer

Work done in first in 3 days = (1/18) + (1/24) + (1/36) = (4 + 3 + 2)/72 = 1/8 ∵ Time taken to complete 1/8 part of work = 3 days ∴ Time taken to complete the whole work = 3 x 8 = 24 days

Question 20

16 children and 24 men complete a certain work for 18 days. If each child takes twice the time taken by a man to finish the work in how many days will 24 men finish the same work?

Accepted Answer

According to the question, 2 children = 1 man ∴ (16 children + 24 men) = (8 + 24) men = 32 men Given M1 = 32, M2 = 24, D1 = 18, D2 = ? and W1 = W2 = 1 According to the formula, M1D1W2 = M2D2W1 ⇒ 32 x 18 x 1 = 24 x D2 x 1 ∴ D2 = (32 x 18)/24 = 8 x 3 = 24 days

Time and Work Questions