Question #1

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?

Work done by X in 4 days =[1/20 * 4] = 1/5

Remaining work =[1-1/5] = 4/5

(X+Y)’s 1 days work= [1/20 + 1/12]

= 8/60= 2/15

Now, 2/15 work is done by X and Y in 1 day.

So, 4/5 work will be done by

X and Y in [15/2 * 4/5] = 6 days

Hence, total time taken = (6 + 4) days

= 10 days

Question #2

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?

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 =1/96 and

Q’s 1 hour’s work =1/80

(P + Q)’s 1 hour’s work

= [1/96 + 1/80]= 11/480

So, both P and Q will finish

the work in 480/11 hrs

Number of days of 8 hours each

=[480/11 * 1/8]=60/11 days= 5 5/11 days

Question #3

A certain number of men complete a piece of work in 60 days.

IF there were 8 men more the work would have been completed

in 10 days less. How many men were there originally?

If there are x workers in first case 1 man will take 60x.

In second it will be 50(x+8)

60x = 50x + 400

x = 40

Question #4

A group of men can complete a job in K hours. After every 4 hours,

half the number of men working at that point of time leave the job.

Continuing this way if the job is finished in 16 hours,

what is the value of K ?

job completed in first 4 hrs = L x 4 = 4L

job completed in next 4 hrs = 4 x L/2 = 2L

job completed in next 4 hrs = 4 x L/4 = L

job completed in last 4 hrs = 4 x L/8 = L/2

4L + 2L + L + L/2 = KL

K = 7+1/2 = 7.5 hours.

Question #5

In the beginning, Ram works at a rate such that he can finish a

piece of work in 24 hrs, but he only works at this rate for 16 hrs.

After that, he works at a rate such that he can do the whole work

in 18 hrs. If Ram is to finish this work at a stretch,

howmany hours will he take to finish this work?

Ram’s 16 hr work = 16/24 = 2/3.

Remaining work = 1 – 2/3 = 1/3.

Using work and time formula:

This will be completed in 1/3 × 18 i.e. 6 hrs.

So, total time taken to complete work = 16 + 6

= 22 hrs.

Question #6

`A can do a piece of work in 10 days, and B can do this work in 15 days. `

They both started together. After three days, B left the work.

In how many more days will the work be finished?

Their combined 3 day work = 3(1/10 + 1/15)

= 3/6 = 1/2.

Remaining work = 1 – 1/2 = ½.

This will be done by A in 1/2 × 10 = 5 days.

Question #7

`A can do a piece of work in 12 days. B can do this work in 16 days. `

A started the work alone. After how many days should B join him,

so that the work is finished in 9 days?

A's work in 9 days = 9/12 = 3/4.

Remaining work = 1/4.

This work was done by B in 1/4 × 16 = 4 days.

∴ B would have joined A after 9 – 4 = 5 days.

Question #8

A and B can do a piece of work in 4 days, while C and D can

do the same work in 12 days. In how many days will A, B, C and

D do it together?

A, B, C and D will together take ¼ + 1/12 =

= 4/12 = 1/3

⇒ 3 days to complete the work.

Question #9

A, B, C, and D can do a piece of work in 20 days. If A and B can

do it together in 50 days, and C alone in 60 days,

find the time in which D alone can do it.

D alone will take 1/20 – 1/50 – 1/60

= 4/300 = 1/75

⇒ 75 days to complete the work.

Question #10

12 men can complete a work in 8 days. 16 women can complete the

same work in 12 days. 8 men and 8 women started working and

worked for 6 days. How many more men are to be added to

complete the remaining work in 1 day?

1 man 1 day work =1/96

1 woman 1 day work = 1/192

Work done in 6 days=6(8/96+8/192)

= 6×18 =3/4

Remaining work = 1/4

(8 men +8 women)'s 1 day work = 1(8/96+8/192)

=1/8

Remaining work =1/4 - 1/8 = 1/8

1/96 work is done in 1 day by 1 man

Therefore, 1/8 work will be done in

1 day by 96 x (1/8) =12 men

You scored 0 out of 10.

Your performance has been rated as