Time and Work- Aptitude Questions and Answers

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A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is?

A)
1/4

B)
4/10

C)
7/15

D)
8/15


Correct Answer :

8/15


Explanation :

A's 1 day's work = 1/15
B's 1 day's work = 1/20
(A + B)'s 1 day's work = 1/15 + 1/20 = (4+3) / 60 = 7/60
(A + B)'s 4 day's work = (7/60) * 4 = 7/15

Therefore, Remaining work = 1 – (7/15) = 8/15

A and B can finish a work 30 days if they work together. They worked together for 20 days and then B left. A finished the remaining work in another 20 days. In how many days A alone can finish the work?

A)
60

B)
50

C)
40

D)
30


Correct Answer :

60


Explanation :

Amount of work done by A and B in 1 day = 1/30
Amount of work done by A and B in 20 days = 20 × (1/30) = 20/30 = 2/3
Remaining work = 1 – (2/3) = 1/3

A finished the remaining work in another 20 days.
So , A completes 1/3 work in 20 days
Amount of work A can do in 1 day = (1/3)/20 = 1/60
A can complete the work in 60 days

3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work?

A)
60

B)
50

C)
40

D)
30


Correct Answer :

40


Explanation :

Work done by 4 men and 6 women in 1 day = 4m + 6w = 1/8---(1)
Work done by 3 men and 7 women in 1 day = 3m + 7w = 1/10 ---(2)

After solving equation (1) and (2) , m=11/400 and w=1/400
Amount of work 10 women can do in a day = 10 * (1/400) = 1/40
i.e, 10 women can complete the work in 40 days

P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. how many days does P alone need to finish the remaining work?

A)
8

B)
5

C)
4

D)
6


Correct Answer :

6


Explanation :

Work done by P in 1 day = 1/18
Work done by Q in 1 day = 1/15
Work done by Q in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6

A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?

A)
75/2 days

B)
22 days

C)
31 days

D)
21 days


Correct Answer :

75/2 days


Explanation :

Work done by A in 20 days = 80/100 = 4/5
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)

remaining work (100-80)=20%
Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = (1/5) / 3 = 1/15 ---(2)

Work done by B in 1 day = Work done by A and B in 1 day -Work done by A in 1 day
=> 1/15 – 1/25 = 2/75

So, B can complete the work in 75/2 days

P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in?

A)
30 days

B)
25 days

C)
31 days

D)
21 days


Correct Answer :

25 days


Explanation :

Work done by P and Q in 1 day = 1/10 , Work done by R in 1 day = 1/50

Thus, Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50
But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can
be written as
Work done by P in 1 day * 2 = 6/50
Work done by P in 1 day = 3/50
i.e. Work done by Q and R in 1 day = 3/50

Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25
So Q alone can do the work in 25 days

A and B can do a piece of work in 72 days, B and C can do it in 120 days, A. and C can do it in 90 days. Who is more efficient?

A)
A

B)
B

C)
C

D)
Can t be determined


Correct Answer :

A


Explanation :

Combined efficiency of A and B =1/72 ...(i)
Combined efficiency of B and C =1/120 ...(ii)
Combined efficiency of A and C =1/90 ...(iii)
Adding Eqs (i), (ii) and (iii),
2 (A + B + C) = 1/72 + 1/120 + 1/90 =(5 +3+ 4) / 360 = 12/360 = 1/30
So, A + B + C =1/60 . ..(iv)

Subtracting Eq. (i) from Eq. (iv), we get
C's efficiency =1/60 - 1/72 = 1/360
Subtracting Eq. (ii) from Eq. (iv), we get
A's efficiency =1/60 - 1/120 = 1/120
Subtracting Eq. (iii) from (iv), we get
B's efficiency =1/60 - 1/90 = 1/180
Cearly, A is most efficient.

5 men can complete a work in 12 days and 9 women take 20 days to complete the same work.How many days will 6 men and 12 women take to complete the work?

A)
8 days

B)
6 days

C)
4 days

D)
7 days


Correct Answer :

6 days


Explanation :

a man can complete the work in (5 *12) days =60 days
a women can complete the work in (9 *20) days= 180 days
a man one day work =1/60
a woman one day work=1/180

(6 men + 12 women) one day work=6 *(1/60) + 12*(1/180) =1 /10 + 1/15 = 5/30 = 1/6
hence, 6 men and 12 women will finish the work in 6 days.

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

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