Dell Time and work Questions

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?
Question Explanation

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?
Question Explanation

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?
Question Explanation

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 ?
Question Explanation

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?
Question Explanation

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?
Question Explanation

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?
Question Explanation

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?
Question Explanation

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.
Question Explanation

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?
Question Explanation

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

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