A Rich Earl And Swamp

A rich earl has become the owner of a piece of land, which to his dissatisfaction turned out to be nothing more than a big swamp. The earl wants to get rid of the swamp. 

A salesman advises him to use his fast-growing plants which can cover the swamp very quickly. "This plant doubles every day, tomorrow you will have two, the day after tomorrow four, etc. In 80 days, your swamp will be completely covered." The earl reacts: "80 days? This takes far too much time. Then just give me eight of these plants."

Question 1: What did the earl think?

Question 2: And what do you think?

Go to the answers directly!

Planting Trees Covering Swamp

What's the exact story? 

The earl must have thought that planting 8 trees on first day itself would cause him to wait for only 10 days. That's totally wrong conclusion.

Though started with 8 trees, on other day number will be doubled only not tripled or increased to x8. Starting with 8 trees is like skipping 3 days (2,4,8) if started with 1 tree.That is only 3 days would be saved. 

In short, with 8 plants, the earl need to wait for 77 days!   

The Dog Of The Commander

A long and straight row of soldiers is marching with constant speed. The dog of the commander runs along the row from the end till the beginning, from the beginning till the end, from the end till the beginning etc. This takes always 2 minutes, 1 minute, 2 minutes, etc. 

At some point the soldiers have to pass a very small bridge. However, the commander does not trust the strength bridge completely. He wonders how much time it will take them to pass the bridge when they stay marching with the same speed. 

How much time is that?  

You can skip to the answer! 

Passing A Very Small Bridge

What is the question?

For march of soldiers to pass any point, there must be first man crossing that point first and then later the last man should cross the same point. 

Now the dog runs from the first to last man in 1 minute, then runs back to first man in 2 minutes and again back to last man in 1 minutes. That means the dog must be at the same point where he started journey from first man. In other words, the dog has run for 2 minutes in both the directions. Hence, he must be at the same point after 4 minutes.

Interestingly, the dog was at first man when started & after 4 minutes ended at the last man of the march. Since dog is at the same point after 4 minutes, the entire march of soldiers is crossed that point in 4 minutes as first and last man have crossed that point.

The same when applied to a very small bridge which can be assumed as a point, we can say that it requires 4 minutes for soldiers to cross it.
 

Draining Reservoir

A large fresh water reservoir has two types of drainage system: small pipes and large pipes.

6 large pipes, on their own, can drain the reservoir in 12 hours.

3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours.

How long will 5 small pipes, on their own, take to drain the reservoir?

Find here the exact time required! 

Time To Drain The Reservoir

Here is the question! 

Let T be the capacity of the tank. Let L be the large pipe and S be the small pipe.

T/6L = 12

L = T/72

T/(3L + 9S) = 8

Putting L = T/72,

S = T/108

Hence T/5S = 108/5 gives S = 21.6 hours.

To conclude, small pipes require 21.6 hours i.e. 21 hours and 36 minutes to drain the reservoir.

Burn The Strings

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is constant and strings are identical.

How do you measure 45 minutes?

That's how to measure 45 minutes!

Timer Using Burning Strings

What was the challenge? 

1. Burn both the ends of 1st string and 1 end of other string.

2. After 30 minutes, 1st string will be burnt out and half of the other string will be burnt out.So far we have counted 30 minutes.

3. Now burn the other end of 2nd end. It will take 15 minute to burnt out totally. This way, we have counted 30 + 15 = 45 minutes using 2 strings.

Time Taken For The Journey

A RED ant is sitting on one side of a table (point X) and a BLACK ant is sitting on the opposite side of the table (point Y).

Now both of them decides to exchange their places and starts crawling. On the way, both of the ants meet and after that, it takes 20 seconds for the RED ant to move to point Y and it takes 5 seconds for the BLACK ant to reach point X.

Find out the total time taken by the RED and the BLACK ant to make the journey.

Here are steps to calculate! 

Source 

Calculation of Time For The Journey

What was the journey?

Let the speed of RED ant is R & that of BLACK ant is B

Let time taken by them to meet be T.

Now we will apply the basic formula of distance:

Distance = Speed * Time.

The RED ant travels R T distance before meeting and 20 R after the meeting.

The BLACK ant travels B T distance before meeting and 5 B after the meeting.

Now as per the question,The distance traveled by RED ant before they both meet will be equal to the distance covered by BLACK ant after they meet. We can say the same for the vice versa case as well.

Thus,

RT = 5B and BT = 20R i.e. B = 20R/T, putting in RT = 5B

R T = [20R/T] * 5

RT = 100R/T

T^2 = 100

T = 10.

Thus the RED ant will require 10 + 20 = 30 seconds to travel the distance.

And the BLACK ant will take 10 + 5 = 15 seconds to travel the distance. 

Time Of Arrival?

One day Rohit decided to walk all the way from city Bangalore to Tumkur. He started exactly at noon. And Samit in city Tumkur decided to walk all the way to Bangalore from Tumkur and he started exactly at 2 P.M. on the same day.

Both met on the Bangalore - Tumkur Road at five past four, and both reached their corresponding destination at exactly the same time.

At what time did we both arrive?

      Beginning of Journey

Find here their arrival time! 

Finding The Time Of Arrival

What was the puzzle? 

Let 'x' km/minute be the speed of Rohit's walk. He started to walk at 12 PM & met Samit at 4:05 PM. That means he has walked for 245 minutes. 

Distance traveled by Rohit = 245x km

Let 'y' km/minute be the speed of Samit's walk. He started to walk at 2 PM & met Samit at 4:05 PM. That means he has walked for 125 minutes.

Distance traveled by Samit = 125y km 

    Time of Meeting

Now after meeting each other they resumed their journey further. That means Rohit continues to Tumkur & covers distance of 125y km at his speed of x km/minute. Time taken by him further to complete the journey is 125y / x minutes (Time = Distance/Speed).

Journey of The Dog

Jessica, Warner decided to meet & left their home. And a puppy starts walking down a road. They started at the same time. Their homes are located at 33 KM away from each other.

• Warner walks at 5 miles/hour.
• Jessica walks at 6 miles/hour.

  

The puppy runs from Warner to Jessica and back again with a constant speed of 10 miles/hour.

 
The puppy does not slow down on the turn. How far does the puppy travel in till Jessica and Warner meet?

Know here the distance traveled by puppy! 

Distance in The Dog's Journey!

What was the puzzle? 

First thing on which we need to focus on in how much time Jessica and Warner would meet. Since they are moving towards each other the distance of 33 KM is being covered at 5 + 6 = 11 KM/h.  So they are going to meet each other in 33/11 = 3 hours. Now everything else here can deceive you to find distance covered by puppy. All you need to do is stick to the basics.

Speed = Distance / Time

Distance = Speed * Time 

Distance covered by Puppy = Speed of Puppy * Time for which it traveled.

Distance covered by Puppy = 10 * 3 = 30 KM 

So Puppy travels 30 KM to & fro until Jessica and Warner meets.