Time and Work- Aptitude Questions and Answers

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A grain stock in a village A runs for 21 days. The same stock can run for 28 days in village B. If both the villages are given the same grain stock, then how long will the stores run?

A)
14 hours

B)
12 hours

C)
7 hours

D)
49 hours


Correct Answer :

12 hours


Explanation :

The quantity of grains used by village A and B in one day = 1/21 + 1/28 = 7/84 = 1/12

Therefore, the stocks will be run out in 12 days by both the villages.

If 15 men take 21 days of 8 hours each to do a piece of work, then what is the number of days of 6 hours each that 21 women would take, if 3 women would do as much as 2 men?

A)

18


B)

20


C)

25


D)

30



Correct Answer :

30


Explanation :

As is given 3W = 2M thus, 21W = 14M

M1 = 15M, D1 = 21, H1 = 8
M2 = 21W = 14M, D2 = ?, H2 = 6

M1*D1*H1 = M2*D2*H2
15*21*8 = 14*D2*6

D2 = 15*21*8 / 14*6
no. days for these women to do the job , D2 = 30

A and B working together can finish a piece of work in 12 days while B alone can finish it in 30 days. In how many days can A alone finish the work?

A)

18 days


B)

20 days


C)

24 days


D)

25 days



Correct Answer :

20 days


Explanation :

A and B do the work in 12 days
One day work of A and B = 1/12
B alone do the work in 30 days
One day work of B = 1/30
One day work of A = 1/12 - 1/30
= 5 - 2/60
= 3/60
= 1/20
A can do the work alone in 20 days.

If 5 men can do a piece of work in 10 days and 12 women can do the same work in 15 days, the number of days required to complete the work by 5 men and 6 women is?

A)

15/2 days


B)

8 days


C)

19/2 days


D)

12 days



Correct Answer :

15/2 days


Explanation :

5 men complete the work in 10 days
5 men, 1 day's work = 1/10

12 women complete the work in 15 days
12 women, 1 day's work = 1/15
6 women, 1 day's work = 1/30

Hence, 5 men & 6 women, 1 day's work = (1/10)+(1/30) = 2/15
They will complete the work in = 15/2 days = 7.5 days

Praful has done 1/2 of a job in 30 days, Sarabjit completes the rest of the job in 10 days. In how many days can they together do the job?

A)

30 days


B)

45 days


C)

15 days


D)

60 days



Correct Answer :

15 days


Explanation :

Praful can complete full Job in= 30 * 2 = 60 days
Sarabjit can completes rest of the job means 1/2 job in 10 days, so full job in= 10 * 2 = 20 days

Their combined one day work =1/60 + 1/20 = 4/60 = 1/15

So, they both take 15 days to complete full Job.

X can do a piece of work in 20 days, while Y can do in 10 days. If Y worked at it for 8 days,then X can finish the remaining work in______.?

A)
2 days

B)
3 days

C)
4 days

D)
5 days


Correct Answer :

4 days


Explanation :

Y's 8 day's work = 8*(1/10) = 4/5
Remaining work = (1 - 4/5) = 1/5
1/5 work is done by X = 20*(1/5) = 4 days

If 80 men can do a piece of work in 10 days, in how many days can 40 men do the same piece of work?

A)

5


B)

20


C)

30


D)

40



Correct Answer :

20


Explanation :

80 men finish work in 10 days
So, 1 man would finish in 80*10 = 800 days
Hence 40 men would finish it in 800/40 = 20 days

Or

M1 * D1 = M2 * D2
80*10 = 40*D2
(80*10)/40 = D2
20 = D2
Therefore it will take 20 days for 40 men to complete same piece of work

If 80 men can do a piece of work in 10 days, how many men are required to do the same work in 4 days?

A)

50


B)

100


C)

200


D)

300



Correct Answer :

200


Explanation :

M1 * D1 = M2 * D2
80*10 = M2*4
(80*10)/4 = M2
200 = M2
Therefore 200 men are required to finish the work in 4 days

OR

80 men finish work in 10 days
So,80*10 = 800 Mens will be required to complete in one single day.
Hence to finish in 4 days, men are required finish 800/4 = 200

18 men can dig a well in 10 days. After they have worked for 4 days, how many more men shall be employed to complete the work in 4 days from then?

A)
3

B)
6

C)
9

D)
18


Correct Answer :

9


Explanation :

Total work = 18 men * 10 days = 180 unit
Work done in 4 days = 18 men * 4 days = 72 unit
Remaining work = 180 - 72 = 108 unit

108 unit work should done in 4 days
(18+X) men * 4 days = 108 unit
(18+X) men = 27
X = 9 men extra require to complete the work in 4 days.

Ram could complete a job alone in 6 days but Sunil would take thrice the time to do it alone.They started the work together but Ram had to leave a few days before the completion of the work and Sunil had to complete the remaining task by himself. If as a result , it took 6.75 days in all to complete the job, for how many days did the duo work together?

A)
4.50

B)
3.75

C)
3

D)
5.25


Correct Answer :

3.75


Explanation :

In 1 day Ram can finish 1/6 of the work.
In 1 day Sunil can finish 1/18 of the work.

together they can do in 1 day (1/6 + 1/18) = 2/9 of the work.

Hence, suppose Ram leaves in x days, then

x*1/6 + (6.75 - x)*1/18 = 1 (the whole work)
x/6 + 6.75/18 - x/18 = 1
x/6 - x/18 = 1 - 0.375
3x/18 = 0.625
x= 3.75

Ram left the job after x days = 3.75 days
i.e., they work together 3.75 days.

A and B can together finish a work in 30 days. They worked at it for 20 days and then B left. The remaining work was done by A alone in 20 more days. B alone can do the entire work in?

A)

60 days


B)

54 days


C)

50 days


D)

48 days



Correct Answer :

60 days


Explanation :

Amount of work done by A and B in 1 day = 1/30
Amount of work done by both in 20 days = 20 * (1/30) = 2/3
Remaining work = 1 - 2/3 = 1/3
Given, A completes 1/3 work in 20 days.
Therefore, A can finish the whole work in (20 x 3) = 60 days.

Work done by A and B in 1 day, A+B = 1/30
A = 1/60 then Work done by B = 1/30 - 1/60 = 1/60
So B alone can finish the work in 60 days.

A certain piece of work can be completed by 12 men in 9 days. After they have worked for six days, six more men joined them. How many days will it take to complete the remaining work?

A)

4


B)

3


C)

2


D)

1



Correct Answer :

2


Explanation :

12 men worked for 9 days, total work = 12 * 9 = 108
Work done in 6 days = 12 *6 = 72
remaining work = 108 - 72 = 36
6 more men joined, total men = 12 + 6 = 18
so, no of days taken = 36 / 18 = 2 days

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