Time and Work - Aptitude Questions and Answers Part 2

6. 3 adults take 2 working days to dig a trench. 4 boys can dig the same trench in thrice the time taken by these 3 adults. How many days will 8 adults and 8 boys working together take to dig the same trench?

a. 3Days
5
b. 3Days
4
c. 1.5 Days
d. 2 days

Answer: a. 3Days
5

Explanation:
In 1 day 3 adults do1amount of work ; So, in 1 day, 1 adult does1/2=1work
236
In 1 day, 8 adults do1x 8 =4amount of work
63
4 boys take thrice the time taken by 3 adults. So, they take 6 days.
In 1 day 4 boys do1amount of work; So, in 1 day, 1 boy does1/6=1work
6424
In 1 day, 8 boys do1x 8 =1amount of work
243
In 1 day, 8 adults and 8 boys do4+1=5amount of work
333
∴ 8 adults and 8 boys together complete the entire work in3days.
5


7. Two friends P & Q take a project and start working on it together. P alone can finish the project in 20 days while Q takes 5 days more than P to finish it. After working together on the project for some days, P has to leave. Q now takes 10 days to finish the remaining project alone.  After how many days of working together did P leave?

a. 5 Days
b. 62Days
3
c. 81Days
5
d. 102Days
5

Answer: b. 62Days
3

Explanation:

Tip:
Understanding and solving such problems is very easy by drawing a line.


time and work
In 1 day P does1work; And in 1 day Q does1work
2025
As seen above, Q works alone for 10 days.
In 10 days Q completes1x 10 =2work
255
Remaining work = 1 -2=3= Done by P and Q together
55
Total Work done = Total days x Work done by all in 1 day
Let P and Q work together for total K days.
3= K x (1+1)
52025
∴ K =20= 62days = Days when P and Q worked together
33
Thus P leaves after 62days.
3


8. If M is asked to work alone on a project, he will require 25 days extra to finish it than the time M and N take to finish it together. However, if N is asked to finish it alone, he will require 1 week and 2 days more to finish it than what M and N would take together. In how many days will M and N finish the project working together?

a. 15 days
b. 18 days
c. 20 days
d. 25 days

Answer: a. 15 days

Explanation:

Let M and N together finish the work in 'X' days.
So, M when working alone takes 25 days more to complete the entire work.
And, N when working alone takes 1 week and 2 days (i.e.) 9 days more to complete the entire work.

Tip: In such cases, use the following trick -

X = Extra days of P x Extra days of Q


∴ X = 25 x 9 = 15 days = Number of days in which M and N together finish the work


9. Working 8 hours a day, A can finish an assignment in 12 days while B takes 2 days less to finish it, working 2 hours more than A, every day. The contractor decides to put them to work together on the assignment,. Each working day now is 8 hours. How many days will they take to finish the assignment?

b.60days
11
c.39days
12
d.15days
8
d. 8 days

Answer: b.60days
11

Explanation:

A completes the work in 12 days at 8 hour per day = 12 x 8 = 96 hours
In 1 hour, A completes1amount of work
96
B completes the work in 8 days (2 days less than A) working 10 hours everyday (i.e. 2 hours more than A per day) = 8 x 10 = 80 hours
In 1 hour, B completes1amount of work
80
Working together, in 1 hour A and B complete1+1=11amount of work
9680480
So they complete entire work in480hours.
11
Since they work for 8 hours per day, they need480x1=60days
11811


10. Working alone, Ram can erect the boundary wall of a land in 16 days but Samar can do the same work in 12 days. Ram and Samar are put to work on that contract on alternate days. In how many days will the boundary wall be ready, if Ram works on first day?

a.24days
7
b.48days
7
c. 12.5 days
d. 133days
4

Answer: d. 133days
4

Explanation:

This sum is very easy to understand and solve
In 1 day Ram does1amount of work
16
In 1 day Samar does1amount of work
12
First day Ram works and Second day Samar.
So in 2 days, Work done =1+1=7amount of work
161248
So in 12 days (i.e. 6 times 2days) work done = 6 x7=42=7
48488
Remaining work =1
8
Now, on 13th day, Ram will work and complete1amount of work
16
Now, work remaining =1-1=1
81616
We know that in 1 day Samar will complete1amount of work
12
1>1
1216
So, how long would Samar take to finish1of work?
16
=1÷1=3
16124
This means that Samar completes remaining work in 3/4th day.
So answer is 13 +3days = 133days
44