### Time and Work

Ramesh is thrice as good a workman as Suresh and together they finish the piece of work in 15 days. In how many days will Ramesh alone finish the work?

18 days

20days

26 days

24 days

Adam’s 1 day’s work: Brain’s 1 day’s work = 3 : 1

(Adam + Brain)’s 1 day’s work = 1/15

Now, divided 1/15 in the ratio 3 : 1

Therefore, Adam’s 1 day’s work = 1/15 × 3/4 = 1/20

Therefore, Adam alone can finish the work in 20 days.

Samir can do a job in 30 days. In how many days can he complete 70% of the job?

18 days

21 days

26 days

24 days

he finishes the work in 30 days, or he can do 100% of the work in 30 days. If he has to do only 70% of the work, he will require 70% of the time. Number of days required = 30 × 70/100 = 21 days.

Reshma can do 75% job in 45 days. In how many days can she complete the job?

55

65

60

58

Reshma does 75% of the work in 45 days. That means she does 1% of the work in 45/75 days and she will do 100% of the work in 100 × 45/75 = 60 days.

John can do a piece of work in 60 days; he will do how much of the work in 40 days?

1/3

2/3

1/2

3/4

Sol: In 1 day, John does 1/60th of the work, so in 40 days he will do 40 × 1/60 = 2/3^{rd} of the work.

Anup can finish a piece of work in 30 days. He will finish what percent of the work in 15 days?

45%

80%

50%

35%

In 1 day, he does 1/30th of the work, and in 15 days, he will do 15/30th of the work which is 100 × 15/30 = 50%.

Ria can do a piece of work in 40 days, she will take how many days to finish three-fourth of the work?

20

25

28

30

Ria can complete the work in 40 days. She will do ¾th of the work in ¾th of the total time. i.e. she will need 40 × 3/4 = 30 days.

A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?

3.75 days

4 days

5 days

6 days

1/6 + 1/10 = 8/30 = 4/15

15/4 = 3.75 days

A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?

20 days

16 days

24 days

28 days

B = 1/8 – 1/2 = 1/24 => 24 days

10 men can complete a job in 14 days. How long will it take 4 men to finish the same job if they work at the same rate?

33 days

35 days

37 days

39 days

M1 = 10, T1 = 14 days

M2 = 4, T2 = ?

T2 = (M1.T1)/M2

= 10 * 14 / 4

35

15 men can complete a job in 10 days. How long will it take 8 men to finish the same job if they work at the same rate.

14 3/4 days

16 3/4 days

18 3/4 days

20 3/4 days

M1 = 15, T1 = 10 days

M2 = 8, T2 = ?

T2 = (M1 * T1) / M2

= (15 * 10) / 8

8 ^{3} ∕ _{4} days

If 9 men need 15 days to complete a task, how many days would it take to complete this task if 3 additional men were employed?

12 1/2

10

11 1/4

6

Men Days

9 15

12 x

9/12 = x/15

x = 11(1/4)

A and B can reap a field in 30 days working together. After 20 days, however B is called away and A takes 20 days more to complete the work. B alone can do the whole work in?

48 days

50 days

56 days

60 days

For A and B, t1 = 20 days

For A, t2 = 20 + 10 days = 30 days

For B, t = ?

1/t = 1/t_{1} - 1/t_{2} = 1/20 - 1/30

3 - 2 / 60 => 1/60

t = 60 days

A can do a piece of work in 10 days and B can do it in 15 days. The number of days required by them to finish it working together is?

8

7

6

4

A -> t1 = 10 days, B -> t2 = 15 days

1/t = 1/t_{1} + 1/t_{2}

1/10 + 1/15

1/6

t = 6

A group of labourers accepted to do a piece of work in 20 days. 8 of them did not turn up for the work and the remaining did the work in 24 days. The original number of labourers was?

47

48

49

50

Men Days

x 20

x-8 24

x / x-8 = 24 / 20

5x = 6x - 48

x = 48

If a certain job can be performed by 18 workers in 26 days, the number of workers needed to perform the job in 12 days is

39

30

24

45

workers days

18 26

x 12

18 / x = 12 / 26

x = 18 * 26 / 12 = 39

A group of students volunteered to finish a construction work in 25 days. 10 of the students did not come and the work could be finished in 35 days. The original number of students in the group were.

25

32

35

37

Men Days

x 25

x-10 35

x / x - 10 = 35 / 25

7x - 70 = 5x

2x = 70

x = 35