# Quantitative Aptitude: Time and Work Set 1

Time and Work Bank PO Questions

1. A and B can complete a job in 16 hrs and 24 hrs respectively. In how many hours they together can produce 10 such jobs?
A) 74
B) 96
C) 82
D) 85
E) None of these
Option B
Solution:

Working together:
1/16 + 1/24 = 5/48
So they complete 5 jobs in 48 hrs.
Therefore, 10 jobs in 48×2 = 96 hrs.
2. 4 men and 5 women can complete a work in 8 days. The same work can be completed by 2 men and 3 women in 14 days. In how many days 1 women will complete the work?
A) 32 days
B) 45 days
C) 38 days
D) 56 days
E) 28 days
Option D
Solution:

4m + 5w = 8d
So 8 × (4m + 5w) = 8/8 d
32m + 40w = 1 …… (1)
Also given:
2m + 3w = 14d
So 28m + 42w = 1 ……(2)Now equate (1) and (2)
32m + 40w = 28m + 42w
Solve, 2m = 1w
Put in any of equations above.2w + 5w = 8d
7 w in 8 days. So 1 w in 7 × 8 = 56 days
3. A and B produced similar chairs. When A worked for 2 hrs and B for 5 hrs, they completed half of the work. Next they worked together for 3 hrs. If 1/20th of the work is yet to be completed, then find in how many hours can B complete the work working alone?
A) 16
B) 18
C) 12
D) 15
E) 22
Option D
Solution:

Let A can complete work in a days and B in b days.
So 2/a + 5/b = 1/2 …..(1)
Now 1/20 work is left after further 3 days. So in 3 days work completed is 1 – (1/2 + 1/20) = 9/20
So 3/a + 3/b = 9/20 ……(2)
Solve equations 1 and 2. b = 15
4. A, B and C can complete a work in 12, 15 and 25 days respectively. A started the work, C and B joined him after 3 and 6 days respectively. How much work did A complete?
A) 3/5
B) 2/3
C) 1/8
D) 3/7
E) None of these
Option B
Solution:

Let total work completed in x days. So A worked for all x days. B for (x-6) days and C for (x-3) days. So
x/12 + (x-6)/15 + (x-3)/25 = 1.
Solving for x, we get x = 8
So A completed x/12 = 8/12 = 2/3rd of work.
5. 16 men can complete a job in 7 days. The same work can be completed by 20 women in 9 days. In how many days 14 men and 15 women can complete the job all working together?
A) 2 1/3 days
B) 7 days
C) 4 4/5 days
D) 8 days
E) 6 1/3 days
Option C
Solution:

16 m in 7 days so 14 m in 16×7/14 = 8 days.
20w in 9 days so 15 w in 20×9/15 = 12 days.
So together 1/8 + 1/12 = 5/24
So 24/5 days.
6. A and B can complete a work in 20 days and 30 days respectively. A starts the job and B joins him on alternate days starting from 2nd day. In how many days they can together complete the work?
A) 10 days
B) 12 2/3 days
C) 14 days
D) 34 days
E) 15 1/5 days
Option E
Solution:

On 1st day A completes 1/20 of work.
On 2nd day, A and B together completes 1/20 + 1/30 = 1/12 of work.
Using LCM method:
Total work = LCM of 20 and 12 = 60
So efficiency of A = 60/20 = 3.
And efficiency of A and B on 2nd day = 60/12 = 5
So in 2 days they complete 3+5 = 8 works
Multiply by 7 both sides.
In 14 days they complete 56 works.
Work left = 60 – 56 = 4
Now on 15th days A, turn. He completes 3 of the work out if 4 left.
Now remaining work = 4 – 3 = 1.
On 16th day, A and B’s turn. So they complete remaining 1 work in 1/5 day.
So total 15 1/5 days.
7. A and B can complete a work in 12 and ‘n’ days respectively. They worked for 3 days and found 3/5th of the work as pending. If C who can complete the same work in 24 days also works with them, how much work will remain uncompleted after 4 days?
A) 8/19
B) 15/31
C) 2/9
D) 3/10
E) 3/13
Option D
Solution:

3/5th is pending means 2/5th is completed. So
(1/12 + 1/n) × 3 = 2/5
Solve, B can complete work in n = 20 days.
Now: in 4 days all A, B, C completed
(1/12 + 1/20 + 1/24) × 4 = 7/10 of work
So pending work = 1 – 7/10 = 3/10 of work.
8. A can complete a work in 24 days. If he is half as efficient as B, then in how many days they both can complete a job working together?
A) 8 days
B) 14 days
C) 17 days
D) 5 days
E) 10 days
Option A
Solution:

A is half efficient so takes double days than B. So B can alone complete job in 12 days.
So together in 24×12/(24+12) = 8 days
9. A can complete 40% of work in 12 days. To complete the remaining work in next 12 days B joins him. How much more efficient is A than B?
A) 80%
B) 200%
C) 50%
D) 100%
E) None of these
Option D
Solution:

A completes 40% of work in 12 days so 60% of the work has to be completed by A and B.
They together take 12 days to complete 60% of work.
So working together, they can complete whole work in 12/60 × 100= 20 days
A completed 40% work in 12 days, he can complete whole work in 12/40 × 100 = 30 days
Let B takes x days to complete whole work. So,
1/30 + 1/x=1/20
Solving we get x = 60
Now A completes whole work in 30 days. B in 60 days so A is twice or 100% efficient than B.
10. A and B together can complete a work in 24/5 days. B and C together can complete a work in 36/5 days. A and C together can complete a work in 72/13 days. In how many days B alone can complete the work?
A) 14 days
B) 12 days
C) 12 1/2 days
D) 19 days
E) 20 days
Option B
Solution:

1/A + 1/B = 5/24 …..(1)
1/B + 1/C = 5/36 ……(2)
1/A + 1/C = 13/72 ……(3)
Add equations 1 and 2 and then subtract 3 from them.
(1/A + 1/B + 1/B + 1/C) – (1/A + 1/C) = 5/24 + 5/36 – 13/72
2/B = 1/6
So B takes 12 days.