Time and Work- Aptitude Questions and Answers

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A and B together can do a work in 8 days. If A alone can do it in 12 days, then in how many days can B alone do it?

A)
12 days

B)
20 days

C)
24 days

D)
28 days


Correct Answer :

24 days


Explanation :

If X can do a piece of work in n days, then X's 1 day's work =1/n
If A and B, working together,and can complete a piece of work in X days. If A, working alone, can
complete the work in Y days, then B working alone, will complete the work in XY/(Y-X) days.

Then ,B alone can complete = (12 * 8) / (12 - 8) = 96/4 = 24 days

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A is twice as good as workman as B and therefore able to finish a piece of work in 30 days less than B. In how many days can they complete the whole work together?

A)
20 days

B)
40 days

C)
60 days

D)
80 days


Correct Answer :

20 days


Explanation :

Let A takes X days to complete the work and B takes 2X days
according to question, A takes 30 days less than B, that is X = 2X – 30
X=30

thus ,A take 30 days to complete the work and B takes 60 days
hence, A and B one days work is 1/30 + 1/60 = 1/20

Therefore, the whole job together they will be completed in 20 days

16 workers working 6 hours day can build a wall of length 150m, breadth 20m, and height 12m in 25 days. In how many days 12 workers, working 8 hours a day will build a wall of length 800m, breadth 15m and height 6m?

A)
50 days

B)
25 days

C)
25 days

D)
60 days


Correct Answer :

50 days


Explanation :

to build a wall of 150*20*12=36000 ,hours required = 16*6*25=2400

to build a wall of 800*15*6=72000 , which is exactly twice as big as the first one,
You need 2400*2 hours = 4800
that is 12*8*days = 4800
days = 4800/96 = 50

A can do a piece of work in 10 days while B can do the same work in 20 days. They start together but A leaves after three days. How many days will B take to complete the remaining work?

A)
14 days

B)
8 days

C)
12 days

D)
11 days


Correct Answer :

11 days


Explanation :

One day's work of A and B = (1/10 + 1/20) = 3/20

Work done by A and B together in the 3 days = 3 (1/10 + 1/20) = 9/20
Remaining Work =1- 9/20 = 11/20

1/20 Work done by B in a day
thus,11/20 Work wll be done by B in (11/20)*20 =11 days

If 3 men or 4 women can reap a field in 30 days, how long will 3 men and 6 women take to reap it?

A)
21 days

B)
16 days

C)
18 days

D)
12 days


Correct Answer :

12 days


Explanation :

3 men can complete work in 30 days
so, Work done by one man in a day = 1/(3*30)
and Work done by one women in a day =1/(4*30))

Thus, 3 men and 6 women will work in a day => 3/(3*30) + 6/(4*30)
= 1/30( 1 + 6/4)
= (1/30)*(10/4) =>1/12

3 men and 6 women do 1/12th part of work in a day,so they will complete the work in 12 days

A is twice as good a workman as B, and finishes the work in 14 days less than B. In how many days can it be done by A alone?

A)
14

B)
21

C)
28

D)
42


Correct Answer :

14


Explanation :

let A take X days to complete the work and B takes 2X days
according to question, A takes 14 days less than B, that is X = 2X – 14 =>14

thus ,A take 14 days to complete the work and B takes 28 days.

30 persons can do a piece of work in 24 days. How many more people are required to complete the work in 20 days?

A)
4

B)
5

C)
6

D)
10


Correct Answer :

6


Explanation :

let X persons required to complete the work in 20 days
then, work done => 30 * 24 = X *20

thus ,num of persons, X = 720 / 20 => 36

extra ,more people required = 36 - 30 = 6 persons

A is twice as good workman as B. Together, they finish the work in 14 days. In how many days can it be finish by B separately?

A)
21

B)
48

C)
42

D)
35


Correct Answer :

42


Explanation :

let A take X days to complete the work and B takes 2X days
(A+B) one day work = 1/X + 1/2X = 1/14
=>14+7=X
=>X=21

Thus ,
B working alone will require 2*21=42 days to complete the work
A working alone will require 21 days to complete the work

A can do a piece of work in 30 days while B can do it in 40 days. In how many days can A and B working together do it ?

A)
70 days

B)
171/4 days

C)
190/7 days

D)
120/7 days


Correct Answer :

120/7 days


Explanation :

If X can do a piece of work in n days, then X's 1 day's work =1/n

Then (A + B)'s 1 day's work = (1/30 + 1/40) = 7/120
Hence, Time taken by both to finish the work = 120/7 days

A can do a piece of work in 20 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in ?

A)
3 days

B)
5 days

C)
7 days

D)
11 days


Correct Answer :

5 days


Explanation :

If X can do a piece of work in n days, then X's 1 day's work =1/n

B's 9 day's work = 9 * (1/12) = 3/4
Remaining work = (1 - 3/4) = 1/4
1/4 work is done by A in = 20 * (1/4) = 5 day

A can do a piece of work in 12 days. B is 60% more efficient than A. The number of days, it take B to do the same piece of work is ?

A)
15/2

B)
25/4

C)
8

D)
6


Correct Answer :

15/2


Explanation :

A's 1 day's work = 1/12
B's 1 day's work = 1/12 + 60% of 1/12 = 1/12 x 160/100 = 2/15

Hence,B can do the work in 15/2 days

X is 4 times more efficient than Y, in what proportion will the number of days taken by X and Y to complete any work?

A)
8 : 1

B)
1 : 5

C)
6 : 8

D)
5 : 1


Correct Answer :

1 : 5


Explanation :

If A is twice as good a workman as B, then:
(a) Ratio of work done by A and B is 2:1.
(b) Ratio of times taken by by A and B to finish a work is 1:2.

Efficiency (X : Y) = 5 : 1
No. of days (X : Y) = 1 : 5

20 persons completed 1/3 rd of the work in 12 days. How many more person are required to finish the rest work in next 12 days?

A)
20

B)
12

C)
18

D)
40


Correct Answer :

20


Explanation :

Work done by 20 persons = 1/3
Remaining work = 1- 1/3 = 2/3
So for double work in same days we need double number of people i.e. 40.

Hence, 20 more people are needed.

6 children and 2 men complete a certain piece of work in six days. Each child takes twice the time taken by a man to finish the work. In how many days will 5 men finish the same work?

A)
6

B)
8

C)
9

D)
15


Correct Answer :

6


Explanation :

6C + 2M = 6 days
36C + 12M = 1 day
As is given 1M = 2C
Then, 36C +12*2C = 1 day
60 children can work in 1 day
Now, 5 men = 10 children
Then, 10 children can work in 6 days.So 5 men also can complete the work in 6 days.

If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same work in 2 days,then the time taken by 15 men and 20 boys in doing the same type of work will be?

A)
4

B)
6

C)
8

D)
9


Correct Answer :

4


Explanation :

Let a man one day work is X and a boy one day work is Y. Then
6x + 8y =1/10
26x + 48y =1/2
After resolving above equations

x =1/100
y =1/200

15x + 20y = 15/100+20/200 = 1/4
Hence, 15 men and 20 boys to do that work in 4 days

6 men or 10 women can reap a field in 15 days, then the number of days that 12 men and 5 women will take to reap the same field is :

A)
5

B)
6

C)
8

D)
12


Correct Answer :

6


Explanation :

Work done by 6 men = work done by 10 women.
Work done by 1 man = work done by 10 / 6 women= 5/3 women

∴ 12 men + 5 women = 12 x ( 5 / 3) + 5 = 25 women
∴ W1 * D1 = W2 * D2 [W = women, D=days]
10 * 15 = 25 * D2
D2 = 6

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

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