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# Time and Work Questions for NMAT:

Download Time and Work Questions for NMAT PDF. Top 10 very important Time and Work Questions for NMAT based on asked questions in previous exam papers.

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Question 1: Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and northwest of B, with BC at 60° to AB. Also, C is located between south and southwest of A with AC at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to

a) 6 : 15 am

b) 6 : 30 am

c) 6 :45 am

d) 7 : 00 am

e) 7 : 15 am

Question 2: In a 4000 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?

a) 20 min

b) 15 min

c) 10 min

d) 5 min

Question 3: A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is $\pi$ r during the first 30 seconds, $\pi$ r/2 during next one minute, $\pi$ r/4 during next 2 minutes, $\pi$ r/8 during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round?

a) 4

b) 8

c) 16

d) 32

Question 4: A can complete a piece of work in 4 days. B takes double the time taken by A, C takes double that of B, and D takes double that of C to complete the same task. They are paired in groups of two each. One pair takes two-thirds the time needed by the second pair to complete the work. Which is the first pair?

a) A and B

b) A and C

c) B and C

d) A and D

Question 5: There’s a lot of work in preparing a birthday dinner. Even after the turkey is in the oven, there’s still the potatoes and gravy, yams, salad, and cranberries, not to mention setting the table.
Three friends — Asit, Arnold and Afzal — work together to get all of these chores done. The time it takes them to do the work together is 6 hr less than Asit would have taken working alone, 1 hr less than Arnold would have taken alone, and half the time Afzal would have taken working alone. How long did it take them to do these chores working together?

a) 20 min

b) 30 min

c) 40 min

d) 50 min

Instructions

Directions for the following five questions: Study the following pie-chart and table to answer the following questions.

<img “=”” alt=”” class=”img-responsive” src=”https://cracku.in/media/radpress/entry_images/5304.png “/>

Question 6: What is the difference in the number of local and non-local students in the university?

a) 188

b) 208

c) 228

d) 248

e) None of these

Question 7: For which course is the number of local students the second highest?

a) A

b) B

c) D

d) F

e) G

Question 8: It takes six technicians a total of 10 hr to build a new server from Direct Computer, with each working at the same rate. If six technicians start to build the server at 11 am, and one technician per hour is added beginning at 5 pm, at what time will the server be completed?
[CAT 2002]

a) 6.40 pm

b) 7 pm

c) 7.20 pm

d) 8 pm

Question 9: Three small pumps and a large pump are filling a tank. Each of the three small pump works at 2/3 the rate of the large pump. If all four pumps work at the same time, they should fill the tank in what fraction of the time that it would have taken the large pump alone?
[CAT 2002]

a) 4/7

b) 1/3

c) 2/3

d) 3/4

Question 10: Three machines, A, B and C can be used to produce a product. Machine A will take 60 hours to produce a million units. Machine B is twice as fast as Machine A. Machine C will take the same amount of time to produce a million units as A and B running together. How much time will be required to produce a million units if all the three machines are used simultaneously?

a) 12 hours

b) 10 hours

c) 8 hours

d) 6 hour

According to given conditions angle between AC and AB is 30 degrees and between AB and BC is 60 degrees. So the triangle formed is a 30-60-90 triangle.

So, total time taken by train is 5 hrs, hence the train reaches at 1 pm. Accordingly, Rahim has to reach C fifteen minutes before i.e. at 12:45 PM.

Time taken by Rahim to travel by car is around 6.2 hrs. So, the latest time by which Rahim must leave A and still be able to catch the train is 6:30 am.

Let A , B and f,s be the distance traveled and speed of the fastest and the slowest person respectively. Also f=2s so in the given time A=2B. Since the ration of the speeds is 2:1, they will meet at 2-1 points = 1 pont.

Both meet each other for first time at starting point . let b travel distance equal to 1 circumference i.e. 1000m so A=2000m . Both meet after 5 min so speed of slowest is 1000/5=200m/min . So speed of the fastest is 400m/min. So time taken by A to complete race 4000/400 = 10 min

Let radius be 1 units and p = 3.14 or $\pi$ . So circumference is $2*\pi$.

According to given condition distance covered in first 1/2 mins = $\pi$/2 km, distance covered in next 1 min = $\pi$/2 km, distance covered in next 2 mins = $\pi/2$ km and finally distance covered in next 4 minutes = $\pi/2$ km.

Time taken to cover first round = 1/2 + 1 + 2 + 4 = 7.5 minutes.

Now time taken to cover $\pi/2$ is in GP.

For the second round the time taken is = 8+16+32+64 = 120

Ratio = 120/7.5 = 16

A takes 4 days to complete the work.
So, B takes 8 days to complete the same work.
C takes 16 days to complete the work.
D takes 32 days to complete the same work.

In order to measure, let the total work be of 64 units. Hence, the speed of working of each of the four persons is given below.

A – 16 units/hr
B – 8 units/hr
C – 4 units/hr
D – 2 units/hr

From the given options, we need to find two pairs in such a way that their speeds are in the ratio 3:2. Note that A+D=18 while B+C=12 and the ratio is 3:2

Hence, the first pair is A and D and the second pair is B and C

Let the time taken working together be t.
Time taken by Arnold = t+1
Time taken by Asit = t+6
Time taken by Afzal = 2t
Work done by each person in one day = $\frac{1}{(t+1)}+\frac{1}{(t+6)}+\frac{1}{2t}$
Total portion of workdone in one day $=\frac{1}{t}$
$\frac{1}{(t+1)}+\frac{1}{(t+6)}+\frac{1}{2t}=\frac{1}{t}$
$\frac{1}{(t+1)}+\frac{1}{(t+6)}=\frac{2-1}{2t}$
$2t+7=\frac{(t+1)\cdot(t+6)}{2t}$
$3t^2-7t+6=0 \longrightarrow\ t=\frac{2}{3}$or $t=-3$
Therefore total time = $\frac{2}{3}$hours = 40mins

Alternatively,
$\frac{1}{(t+1)}+\frac{1}{(t+6)}+\frac{1}{2t}=\frac{1}{t}$
From the options, if time $= 40$ min, that is, $t = \frac{2}{3}$
LHS = $\frac{3}{5} + \frac{3}{20} + \frac{3}{4} = \frac{(12+3+15)}{20} = \frac{30}{20} = \frac{3}{2}$
RHS = $\frac{1}{t}=\frac{3}{2}$
The equation is satisfied only in case of option C
Hence, C is correct

Required difference = (4/22×11+2/16×20-2/8×8+6/76×19+2/24×15-6/20×10+1/17×17)×64
=2(2+5/2-2+3/2+5/4-3+1)×64
=(2+5/4)×64=128+80=208.
Choice (b)

The number of local students studying course:
A-13/22×11×64=6.5×64
B-9/16×20×64=45/4×64
D-41/76×19×64=41/4×64=10.25×64
F-7/20×10×64=3.5×64
G-3/17×17×64=9×64
∴ ‘D’ has the second highest number of local students. Choice (c)

Let the work done by each technician in one hour be 1 unit.
Therefore, total work to be done = 60 units.
From 11 AM to 5 PM, work done = 6*6 = 36 units.
Work remaining = 60 – 36 = 24 units.
Work done in the next 3 hours = 7 units + 8 units + 9 units = 24 units.
Therefore, the work gets done by 8 PM.

Let the work done by the big pump in one hour be 3 units.
Therefore, work done by each of the small pumps in one hour = 2 units.
Let the total work to be done in filling the tank be 9 units.
Therefore, time taken by the big pump if it operates alone = 9/3 = 3 hours.
If all the pumps operate together, the work done in one hour = 3 + 2*3 = 9 units.
Together, all of them can fill the tank in 1 hour.
Required ratio = 1/3

And C’s efficiency is putting A and B together i.e. = 20 hours $( (\frac{1}{60} + \frac{1}{30})^{-1})$
$\frac{1}{x} = \frac{1}{20} + \frac{1}{30} + \frac{1}{60}$