Time and Work- Aptitude Questions and Answers

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6 men and 10 children can do a piece of work in 24 days. A child takes double the time to do a work than the man. In how many days 8 men can complete the work?

A)
33 days

B)
36 days

C)
32 days

D)
39 days


Correct Answer :

33 days


Explanation :

2 children = 1 man then, (6 men + 10 children) = 11 men
Let the required number of days be X.
Less men, More days (Indirect Proportion)
Men Days 11*24 =8*X

X =(11*24)/8 = 33 days

A can do a piece of work in 30 days. He works at it for 20 days but leaves the task incomplete. B takes over and completes it in 12 days. If A and B had worked together, how many days would it have taken them to complete the work?

A)
177/11 days

B)
180/11 days

C)
183/11 days

D)
186/11 days


Correct Answer :

180/11 days


Explanation :

A’s one day’s work=1/30
in 20 days,A will work=20/30=2/3 work
Now, B will do remaining work = 1 – 2/3 = 1/3 in 12 days.
So, B alone will complete the work in 12*3= 36 days
If A and B work together, their one day’s work = 1/30 + 1/36 = (6+5)/180 = 11/180.

Therefore, the whole work will be completed in 180/11 days

A can do a work in 20 days and B can do the same work in 30 days, in how many days will they complete the work together?

A)
16 days

B)
14 days

C)
10 days

D)
12 days


Correct Answer :

12 days


Explanation :

A's one day work = 1/20
B's one day work = 1/30

(A+B)'s one day work = 1/20 + 1/30 = 5/20 = 1/12
Hence, both complete the work together in 12 days

A can do 1/6 part of a work in 5 days, and B can do 2/5 part of the same work in 8 days. How many days can A and B complete the work together?

A)
12 days

B)
13 days

C)
15 days

D)
20 days


Correct Answer :

12 days


Explanation :

A can do 1/6 part of a work =5 days
hence A can complete work =30 days

B can do 2/5 part of a work =8 days
hence B can complete work =20 days

(A+B)'s one day work = 1/20 + 1/30 = 5/60 = 1/12
Hence, both complete the work together in 12 days

A, B and C can complete one task alone in 10 days, 12 days and 15 days respectively. If they start working together, then the number of days required to complete the work?

A)
12 days

B)
10 days

C)
8 days

D)
4 days


Correct Answer :

4 days


Explanation :

(A+B+C)'s one days work= 1/10 + 1/12 + 1/15 = 6+5+4/60 = 15/60 = 1/4
Hence, (A+B+C) can work together in 4 days

45 people can complete work in 16 days. After 4 days of starting work by them, 36 people got together with them. How long will it take to complete the remaining work?

A)
6 days

B)
8 days

C)
20/3 days

D)
31/4 days


Correct Answer :

20/3 days


Explanation :

∴ work will remain the same 45*16 = 45*4 + (45+36)*d
45*16 = 45*4 + (45+36)*d
81*d = 720 - 180
d = 540/81
d = 20/3

Some people can do one work in 12 days. How many days will the double man complete half the work?

A)
9 days

B)
6 days

C)
5 days

D)
3 days


Correct Answer :

3 days


Explanation :

∴ M1*D1/W1 = M21*D2/W2
M*12 / 1 = 2*M*D / 1/2
M*12 = 4*M*D
D= 12/4 = 3

While working 8 hours per day, Anu can prepare a book in 18 days. If the same work has to be completed in 12 days, how many hours will Anu work every day?

A)
12 hours

B)
10 hours

C)
11 hours

D)
13 hours


Correct Answer :

12 hours


Explanation :

The work done by Anu in 18 days working 8 hours per day, would be equal to the work done by her in 12 days working X hours per day.

∴ 18*8 = 12*X
X = 18*8/12 = 12 hours per day

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

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