Magical Water Well & Pilgrim

In a small town, there are three temples in a row and a well in front of each temple. A pilgrim came to the town with certain number of flowers.

Before entering the first temple, he washed all the flowers he had with the water of well. To his surprise, flowers doubled. He offered few flowers to the God in the first temple and moved to the second temple. Here also, before entering the temple he washed the remaining flowers with the water of well. And again his flowers doubled. He offered few flowers to the God in second temple and moved to the third temple. Here also, his flowers doubled after washing them with water. He offered few flowers to the God in third temple.

There were no flowers left when pilgrim came out of third temple and he offered same number of flowers to the God in all three temples. What is the minimum number of flowers the pilgrim had initially? How many flower did he offer to each God?

Click here to know answers! 

Source 

Flowers Owned By Pilgrim

What are the questions? 

Let's assume that the pilgrim had X number of flowers initially. Suppose that he offered Y flowers to the each God. 

Before entering into the first temple, magical well doubled the flowers he had initially. That means he had 2X flowers before entering into first temple. After offering Y flowers, he had 2X - Y flowers.

Again after visiting first temple he washed flowers in magical well where number of flowers gets doubled. Now, he had 4X - 2Y.

Out of these 4X - 2Y, he offered Y flowers to God in second temple. So he had 4X - 2Y - Y = 4X - 3Y flowers after visiting second temple.

These 4X - 3Y doubled to 8X - 6Y after washing in magical water well. 

At third temple, he offered all the flowers he had which in turn equal to Y as we assumed.

8X - 6Y = Y

8X = 7Y

X/Y = 7/8

This is the ratio of the flowers that pilgrim had to the flowers he offered to each God.

In general, the pilgrim had 7N flowers initially and he offered 8N flowers to each God, where N = 1, 2, 3, 4,

Let's cross verify same with N = 1, meaning that the pilgrim had 7 flowers initially & offered 8 flowers to each God.

Before entering into first temple, the flowers doubled to 14. Out of which, 8 offered at first temple & left 6.

Again 6 doubled to 12 at magical well & 8 out of 12 offered to God at second temple leaving behind 4.

Those 4 again doubled to 8 by magical well & all 8 offered to God at third temple. 

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. 

Flip The Triangle

Here you see a triangle formed by ten coins. The triangle points upwards. How can just three coins be moved to make the triangle point downwards?

Flip It By Moving 3

 Here are pointed those 3 coins 

Flipped The Triangle!

What's the challenge? 

Here should be those 3 coins that you need to move so that the triangle point towards down.

And after moving those coin, it will look like,

Distance Between Houses?

Four friends built a colony for themselves. They built their own houses at different
distances from each other.

Chris lived 60 km away from Alex.
Darren lived 40 km away from Bill.
Chris lived 10 km nearer to Darren than he lived to Bill.

Can you find out how far was Darren's house from Alex?

Click here to know the distance!