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QUESTION: 1

P can do 2/5 of the work in 10 days and Q can do 4/5 of the work in 16 days. If both of them start working together then the time in which the work can be done?

Solution:

P can complete the work in 25 days and Q can complete the work in 20 days. So both will complete the work in (20*25)/45 = 100/9 days

QUESTION: 2

A does half as much work as B does in one sixth of the time. If together they take 20 days to complete the work, then what is the time taken by B to complete the work independently.

Solution:

Let B take X days to complete the work then in one –sixth of the time i.e. x/6 days. Now A do half work as done by B so A will take twice the time i.e. 2*x/6 = x/3 to complete the job alone

So 1/x + 3/x = 1/20, x = 80 days

QUESTION: 3

A contractor undertakes to make a mall in 60 days and he employs 30 men. After 30 days it is found that only one- third of the work is completed. How many extra men should he employ so that the work is completed on time?

Solution:

Let total work is w and it is given that one-third of the work is completed after 30 days. Means

M*D = 30*30 = w/3, so total work = 30*30*3

2700 = 30*30 + (30+p)*30, so we get P = 30 (p = additional men)

QUESTION: 4

50 men could complete a work in 200 days. They worked together for 150 days, after that due to bad weather the work is stopped for 25 days. How many more workers should be employed so as to complete the work in time?

Solution:

Let additional workers be P,

(50*150)/(50*200) = 3/4 of the work is already completed and now only 1/4 of the work is to be done. So,

1/4 = ((50 + P) * 25)/50*200, solve for p, we get P = 50

QUESTION: 5

P and Q were assigned to do a work for an amount of 1200. P alone can do it in 15 days while Q can do it in 12 days. With the help of R they finish the work in 6 days. Find the share if C.

Solution:

1/15 + 1/12 + 1/c = 1/6, we got C = 60 (it means C will take 60 days to complete the work alone)

so ratio of work done by P:Q:R = 4:5:1

so c share = (1/10)*1200 = 120

QUESTION: 6

A can do a work in 32 days. P who is 60 percent more efficient than A. Find how much time they will take together to do the same work?

Solution:

A’s one day work = 1/32 so P one day work = (160/100)*1/32 = 1/20, so P will take 20 days to complete the work.

So Both A and P will take = (32*20)/52 = 160/13 days

QUESTION: 7

P does half as much work as Q in three-fourth of the time. If together they take 24 days to complete the work, how much time shall P take to complete the work?

Solution:

Let Q take x days to complete the work, so P will take 2*3/4 of X day to complete the work i.e. 3x/2 days

1/x + 2/3x = 1/24, we get x = 40 days, so P will take = 3/2 of 40 = 60 days

QUESTION: 8

X and Y can do a piece of work in 12 and 15 days respectively. They began their work but before 3 days of its completion Y left. In how many days the work will be completed.

Solution:

(1/12 + 1/15)*(T – 3) + 3/12 = 1

QUESTION: 9

Neha takes 5 hours to type 40 pages while sunil takes 6 hours to type 60 pages. How much time will they take working together on different computer to type an assignment of 180 pages.

Solution:

In one hour number of pages type by neha = 40/5 = 8 and similarly for sunil it is 60/6 = 10.

Now to type 180 pages they will take, (8 + 10)*T = 180, T = 10 hours

QUESTION: 10

P and Q together can complete a job in 90days, Q and R takes 60 days to complete the same work and P and R will take 45 days to complete the same work. How much time will P, Q and R will take to complete the work together.

Solution:

(1/90 + 1/60 + 1/45)*1/2 = (1/P +1/Q + 1/R) = 1/40

so 40 days

QUESTION: 11

A piece of work has to be completed in 50 days, a number of men are employed but it is found that only half of the work is done in 30 days, then an additional 20 men were joined to complete the work on time. How many men initially put to work?

Solution:

suppose Initially X men get employed. Half work is done in 30 days it means full work will be done by X men in 60 days. Now,

Work done = 1/2 = [20*(x + 20)]/60X

X = 40

QUESTION: 12

P does half as much work as Q in three-fourth of the time. If together they take 36 days to complete the work, then the time taken by Q alone to do the work.

Solution:

Suppose Q take ‘X’ days to complete a job, so to do the same work P will take 2* (3x/4) = 3x/2 days.

1/x + 2/3x = 1/36

X = 60

QUESTION: 13

If 20 women and 10 boys can reap a field in 30 days, then in how many days 15 women and 30 boys will reap the field. It is given that work done by 4 women is equal to work done by 3 boys.

Solution:

20w + 10b = 1/21 (work done by 20 women and 10 boys in one day)

It is given that 4w = 3b

Solve both equation to find the value of w and b,

Then, 15/w + 30/b = 1/d (the days in which 15 women and 30 boys complete the work)

QUESTION: 14

If P can do a work in 6 days and Q can do the same work in 8 days. If R who can do the same work in 12 days, joins them, then the work will be completed in how many days?

Solution:

1/6 + 1/8 + 1/12 = 1/d.

D = 8/3 days

QUESTION: 15

A, B and C are three friends that take 20 days to finish a work. The time taken by B is twice the time taken by A and C together and time taken by C to do the work is thrice the time taken by A and B together. How much time will be taken by A alone to do the work.

Solution:

1/a + 1/b + 1/c = 1/20 (given)

In first case let time taken by A and C together is p days, then the time taken by B will be 2p. Substitute in the above equation and we get p = 60 (time taken by B to complete the work).

Similarly in the second case, u will get P = 80 (time taken by C to complete the work)

Now, 1/a = 1/20 – 1/60 – 1/80 to get the answer

QUESTION: 16

If 4 boys or 5 women can reap a field in 20 days. Then what will be the time taken by 6 boys and 8 women to reap the field.

Solution:

work done by one boy in one day = 1/(4*20) Similarly for women = 1/(5*20) Now the time taken by 6 boys and 8 women to reap the field = 6/80 + 8/100 = 1/d (d = 200/31 will be the answer)

QUESTION: 17

5 men and 10 boys can do a piece of work in 30 days and 8 men and 12 boys can do the work in 20 days then the ratio of daily work done by a man to that of boy.

Solution:

5m + 10b = 1/30 and 8m + 12b = 1/20

after solving we get m = 1/200 and b = 1/1200

so required ratio = (1/200) : (1/1200) = 6:1

QUESTION: 18

A certain number of men take 45 days to complete a work. If there are 10 men less then they will take 60 days to complete the work. Find the original number of men.

Solution:

Let initially there are X men. Then x*45 = (x-10)*60. So we get x = 40

QUESTION: 19

Prakash is twice as fast as sumit and therefore Prakash is able to finish the work in 30 days less than sumit. Find the time in which they can complete the work when both are working together?

Solution:

Let sumit take x days then Prakash will take x/2 days to complete the work.

X – X/2 = 30, X = 60

1/60 + 1/30 = 1/d so, we will get d= 20 days

QUESTION: 20

4 women and 5 men working together can do 3 times the work done by 2 women and one man together. Calculate the work of a man to that of woman.

Solution:

4w + 5m = 3*(2w + m)

i.e. 2w = 2m

so ratio of work done by man to woman is 1:1

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