Quiz 2

Question 1

A chemical plant has four tanks (A, B, C and D), each containing 1000 litres of a chemical. The chemical is being pumped from one tank to another as follows: From A to B @ 20 litres/minute From C to A @ 90 litres/minute From A to D @ 10 litres/minute From C to D @ 50 litres/minute From B to C @ 100 litres/minute From D to B @ 110 litres/minute Which tank gets emptied first and how long does it take (in minutes) to get empty after pumping starts?

16.66

30.43%

22

20.77%

20

39.13%

25

9.66%

  • PrepInsta Explanation
  • User Explanation

The change in the amount of chemical in each tank after every minute is as follows: A:

−20–10+90=60 B:−100+110+20=30 C:−50−90+100=−40 D:−

110+10+50=−50

Since tank D loses the maximum amount of chemical in a minute, it will be emptied first. Let n minutes be the time taken by tank D to get empty.

∴1000–50n=0 ∴n=20minutes

Hence, option 3.

Question 2

It takes 6 technicians a total of 10 hours 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 complete?

6:40 pm

20.45%

7:00 pm

23.3%

7:20 pm

19.89%

8:00 pm

36.36%

  • PrepInsta Explanation
  • User Explanation

6 technicians → 10 hours to 1 job

1 technician → 60 hours to 1 job

In 6 hrs (11 a.m. - 5 p.m.)  

In the hour after 5p.m.,

In the next hour, 9 technicians will complete

At the end of 9th hour i.e. 8:00 p.m. the work is complete.

Hence, option 4 is the correct one.

Question 3

In a book store, each of the word of the glowsign board "MODERN BOOK STORES" is visible after 5/2, 17/4 and 41/8 seconds respectively. Each of them is put off for 1 second. Find the time after which one person can see a completely visible glowsign board.

73.5 seconds

28.1%

79.4 seconds

20.92%

68.2 seconds

21.57%

None of these

29.41%

  • PrepInsta Explanation
  • User Explanation

Solution:

The words MODERN, BOOK and STORES appear after 5/2, 17/4 and 41/8 seconds respectively and are put off after 1 second.

So, if all the words flashed together at t = 0 seconds,

then MODERN will flash after (5/2 + 1) = 7/2 seconds

BOOK will flash after (17/4 + 1) = 21/4 seconds

STORES will flash after (41/8 + 1) = 49/8 seconds.
So, all the words will flash together again after LCM(7/2, 21/4, 49/8) seconds

Hence, option 1 is the correct one

Question 4

In Nuts And Bolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts. Another machine produces only bolts at the rate of 75 bolts per minute and needs to be cleaned for 10 minutes after production of every 1500 bolts. If both the machines start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?

130 minutes

18.35%

135 minutes

30.38%

170 minutes

23.42%

180 minutes

27.85%

  • PrepInsta Explanation
  • User Explanation

Question 5

A chemical plant has four tanks (A, B, C and D), each containing 1000 litres of a chemical. The chemical is being pumped from one tank to another as follows:

From A to B @ 20 litres/minute
From C to A @ 90 litres/minute
From A to D @ 10 litres/minute
From C to D @ 50 litres/minute
From B to C @ 100 litres/minute
From D to B @ 110 litres/minute

Which tank gets emptied first and how long does it take (in minutes) to get
empty after pumping starts?

A, 16.66

11.18%

C, 20

21.05%

D, 20

61.84%

D, 25

5.92%

  • PrepInsta Explanation
  • User Explanation

The change in the amount of chemical in each tank after every minute is as
follows:
A:−20–10+90=60
B:−100+110+20=30
C:−50−90+100=−40
D:−110+10+50=−50
Since tank D loses the maximum amount of chemical in a minute, it will be
emptied first.
Let n minutes be the time taken by tank D to get empty.
∴1000–50n=0
∴n=20minutes
Hence, option 3.

Question 6

It takes 6 technicians a total of 10 hours to build and program a new server from Direct Computer, with each working at the same rate. If six technicians start to build the server at 11:00 AM, and one technician per hour is added beginning at 5:00 PM, at what time will the server be complete?

7:30 PM

4.52%

7:45 PM

2.58%

8:00 PM

85.81%

9:00 AM

7.1%

10:00 PM

0%

  • PrepInsta Explanation
  • User Explanation

Let the rate for each technician = 1 unit per hour, implying that the rate for 6 technicians = 6 units per hour.
Since 6 technicians take 10 hours to produce a server, the total job = (rate for 6 technicians)(number of hours) = 6*10 = 60 units.

From 11am to 5pm -- a total of 6 hours -- the amount of work produced by 6 technicians = (rate for 6 technicians)(number of hours) = 6*6 = 36 units.
Remaining work = 60-36 = 24 units.

Starting at 5pm, one worker is added every hour, implying that the rate increases every hour by 1 unit.
Thus:
From 5-6pm, 7 units are produced.
Remaining work = 24-7 = 17 units.
From 6-7pm, 8 units are produced.
Remaining work = 17-8 = 9 units.
From 7-8pm, 9 units are produced.
Remaining work = 9-9 = 0 units.

Since no units remain, the server is finished by 8pm.

Question 7

There are two water drums in my house whose volumes are in the ratio 1:5. Every day the smaller drum is filled first and then the same pipe is used to fill the bigger drum. Normally by the time i return from my college, i.e, at 1:30pm, the smaller drum would just be full. But today i returned a little early and started drawing water from the well with the help of a bucket, poured one-third into the smaller drum and the remaining into the bigger drum. I continued this till the smaller drum was filled. Immediately after that i shifted the pipe into the bigger drum and went for lunch. today if the bigger drum was filled in 12min before its normal time, when was the smaller drum full?

1: 18pm

23.19%

1: 28pm

14.49%

1: 26pm

23.91%

cannot be determined

38.41%

  • PrepInsta Explanation
  • User Explanation

Ans. c. The drums got filled early because of the bucket of water poured. Since the water was poured in the two buckets in the ratio of 1:2, so the time saved should be proportional to that. Total time saved is 12 min. Which means 4 mins saved from smaller drum and 8 mins saved from bigger drum. So the smaller drum will be filled at 1:26.

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