Saturday, January 13, 2018

Mixture of Coffee and Tea

Suppose we lay down two cups in front of you. One of the cups is filled with tea and the other one with coffee. Now we ask you to take a spoonful of tea and mix it with the coffee. 

At this moment, the coffee cup has a mixture of tea and coffee. You have to take that mixture (spoonful) and add it back to the tea. 

Can you now tell if the cup of coffee has more tea or the cup of tea has more coffee ?

Skip to the answer! 

Component Levels in Mixture

How mixture made?

After adding 1 spoon of tea into coffee, the levels of liquids in both cups must be unequal. Whatever now tea cup is missing is now in cup of coffee & mixed with coffee. The content of tea in the cup of coffee is certainly more.

Now after taking spoonful of the mixture back to tea cup the levels of the liquid in both cups would be same. Hence, whatever the cup of tea is missing is replaced by coffee. That missing tea content is now in the cup of coffee where it has replaced some of coffee content! 

Suppose there are 1000 molecules in each cup i.e. of tea & coffee. Let's assume 100 molecules of tea are mixed to coffee using spoon. Now, coffee cup will have 1100 molecules and tea will have 900 molecules. Obviously, right now the cup of coffee contains more tea (100 molecules) that coffee in cup of tea (0 molecules)!

Now while taking 100 molecules back from mixture having 1100 molecules, suppose 70 molecules of coffee & 30 of tea are taken. That means, exactly 100 - 30 = 70 molecules of tea left in mixture. That 70 + 30 molecules mixture is poured into cup of tea. That is exact 70 molecules of coffee mixed in tea.

What does it mean? 70 molecules of coffee have displaced 70 molecules of tea into cup of coffee maintaining level of both the liquids. 

We can say other way as well. 30 molecules of tea displaced 30 molecules of coffee into cup of tea while maintaining levels of both the liquids same. 

So the answer is both have same level of contents mixed.

Knowing Component Levels in Mixture

Monday, January 8, 2018

An Insepection by The Superintendent

One day, a class teacher was told that the school superintendent will be visiting her class on the next day. The superintendent can ask questions from anywhere and it can be easy as well as difficult. The teacher will have the liberty to choose any pupil for answering the question.

How to impress the Superintendent?

Now she is determined that the impression that is cast upon the superintendent after the inspection should be great. How will she instruct the students so that she maximizes the chances of receiving a correct answer for each question? Also, she must create the best impression. How will she do it? 

This is what she should do! 

To Impress Superintendent

What was the resolution of teacher? 

Now what should teacher do here is to devise the 'sign' language to communicate with students. Also she needs to make sure that the superintendent won't have any doubt while questioning students.

She should ask all the students to raise hands for every question that is being asked by superintendent. However, those who know correct answers should raise right hand & rest of all should raise left hand. This way she would be able to know the students who knows the correct answer & choose any of them to answer the question.

All raised hands to each question would definitely leave great impression on the superintendent.

Sign language to communicate while inspection

Note : We are assuming superintendent not smart enough to notice that students raising different hands for different questions.

Saturday, January 6, 2018

Generous Devotee

A devotee visits 9 temples when he visits India. All these nine temples have one thing in common - there are 100 steps in every temple. The devotee puts Re.1 coin after climbing up every step. He does the same while climbing down every step. At each temple, the devotee offers half of his money from his pocket to god. In this way, his pocket becomes empty after his visit to 9th temple.

How much donated by the devotee?

Can you calculate the total amount he had initially ? 

Click here to know exact amount! 

Donations By The Devotee

Why to calculate those?

Using algebraic equations in the case can make things complicated unnecessarily. Hence, we would start from backward. Before putting 100 coins on steps while climbing down 9th temple devotee must had 100 coins. That means he had 200 coins when he climbed up the 9th temple half of which i.e. 100 he offered to that temple & 100 put on the 100 steps of 9th temple. Moreover, he must have placed 100 coins while climbing up 9th temple. So before visit to 9th temple he must had, (100 x 2) + 100 = 300 coins.

Same way, finding the amount he had before visit to each temple like below.

Before eight temple: (300+100)*2 + 100 = 900
Before seventh temple: (900+100)*2 + 100 = 2100
Before Sixth temple: (2100+100)*2 + 100 = 4300
Before fifth temple: (4300+100)*2 + 100 = 8900
Before fourth temple: (8900+100)*2 + 100 = 18100
Before third temple: (18100+100)*2 + 100 = 36,500
Before second temple: (36500+100)*2 + 100 = 73300
Before first temple: (73300+100)*2 + 100 = 146900

Calculation of Donations By The Devotee
To conclude,  he had Rs. 146900 initially.  


Friday, January 5, 2018

Test of an Examiner

Five students - Adam, Cabe, Justin, Michael and Vince appeared for a competitive exam. There were total five questions asked from them from which were two multiple choice questions (a, b or c) and three were true/false questions. Their answers are given as follows:

Cabe c b True True False

Adam c c True True True

Justin a c False True True

Michael b a True True False

Vince b c True False True

Also, no two students got the same number of correct answers. Can you tell the correct answer? Also, what are their individual score?

Knowing Correct Answers And Evaluating Scores

Responding To Test of an Examiner

What was the test?

There are 2 possibilities of scores & that are either 0,1,2,3,4 or 1,2,3,4,5. First of all, let's arrange students' responses in order like below.

Assessment of students' responses
Table 1

What we notice here is that, there are few responses to same question by different student matching.

For the Question III, only Justin given different answers than other.

Case 1 : If we assume Justin's answer is correct then rest of all are wrong in response to Question III. That means either maximum score in test is 4 or Justin himself has scored 1 to 5.

Let's test that apart from Justin who can have score of 4. If any body other scores 4 then he must share at least 3 similar answers with other (excluding Answer III; refer image below). Only Adam has exact 3 matching responses with Justin.

Assessment of students' responses
Table 2

If Adam's score is 4 (Answers to I, II, IV, V are correct) then, Justin too would score 4 (Answers to II, III, IV,V are correct) since Adam & Justin have same responses to Questions II, IV,V).
If nobody scoring as 4 then Justin can have score of 4 or 5.

Case 1.1 : If his score is 4 then there has to be somebody has to be there scoring 0. Now Vince and Adam has at least 2 responses matching with the Justin. That means they can't score 0 since even 1 answer is wrong as Justin the other must be correct as Justin. Michael or Cabe can have 0 score in the case. If anybody of them has score 0 then answer as a TRUE to the Question IV is incorrect i.e. correct Answer IV is FALSE. So Justin is WRONG in Answer IV only. In short, a, c, FALSE, FALSE, TRUE is correct combination of answers. But thing is here in the case both Michael and Cabe would have score 0! Hence Justin's score can't be 4 too.

Case 1.2 : If Justin's score is 5, then a, c, FALSE, TRUE, TRUE are the right answers. No one would score 4 in that case with 3 as second highest by Adam.

Wednesday, January 3, 2018

A Check Post At Each Mile

A poor villager grows mango in his land and sells them in the town. The town is 1000 miles away from the village. He has rented a truck for transporting the mangoes to the town. The truck can carry 1000 mangoes at one time and this season, he was able to yield 3000 mangoes.

There is a problem. At each mile till the town, there is a check post at which he must give one mango each while traveling towards the town. However, if he is traveling from the town towards his village, he won’t have to give anything.

Dealing at the every chech post per mile!
Transportation Truck

Tell a way in which the villager can take highest possible number of mangoes to the town.

Smart Saving At Check Posts

How much each check post charging?

Obviously, he can't make 3 trips from town to village straightaway as in that case he wouldn't have anything left (3 x 1000 mangoes paid).

So he need to divide the journey into parts. While breaking journey into parts he has to make sure that after each part he will need less trips to complete the next part.

Now if somehow he pays 1000 mangoes in first part of the journey then for next part he has to make only 2 trips to carry 2000 mangoes.

Part 1 : Hence, he should first make 3 trips till 333 miles. In this part, he would pay 3 x 333 = 999 mangoes leaving 3000 - 999 = 2001 mangoes in stock.

Taking 3000 Mangoes Across 1000 Miles Smartly!
Part : 1

Part 2 : He should leave 1 mango here & take 2000 mangoes further. For next part, he need to make at least 2 trips for 2000 mangoes. In order to save number of trips in next part some how he need to make mangoes in stock less than 1000. For that he should make 2 trips 500 mile further. So he will pay 2 x 500 = 1000 mangoes but having 2000 - 1000 = 1000 mangoes in stock. Still he has to travel 1000 - 500 - 337 = 167 miles.

Taking 3000 Mangoes Across 1000 Miles Smartly!
Part : 2

Part 3 : For next 167 miles, he need to make only 1 trip of 1000 mangoes where he will pay 167 mangoes leaving 1000 - 167 = 833 mangoes. 

Taking 3000 Mangoes Across 1000 Miles Smartly!
Part : 3
This is how he can save 833 mangoes in entire journey. 


Tuesday, January 2, 2018

An Experimental Professor

An eccentric professor used a unique way to measure time for a test lasting 15 minutes.
He used just two hourglasses. One measured 7 minutes and the other 11 minutes.

During the whole time he turned the hourglasses only few times. 

Measure 15 minutes usnig 7 & 11 minutes hourglasses

How did he measure the 15 minutes?

Couple of methods to count 15 minutes. 

15 Minutes Countdown

What was the challenge?

There were 2 ways for professor to count 15 minutes using 11 & 7 minutes hourglasses.

Method 1 :

1. He started both 7 & 11 minutes hourglasses but didn't begin test.

2. After 7 minutes hourglass ran out, he started the test. Still 11 one yet to count 4 minutes.

3. After conducting test for 4 minutes, 11 hourglass ran out.

4. Now he turns around 11 hourglass & continues. So 11 + 4 = 15 minutes counted.

Counting 15 minutes using 7 & 11 minutes hourglasses
Method 2 :

1. He started both the hourglasses & started to conduct the test as well.

2. When 7 minutes ran out he turned around it & kept 11 minutes counting.

3. After 4 minutes, 11 minutes hourglass ran out. Meanwhile 7 minutes hourglass also counted 4 minutes. So far 11 minutes counted.

4. Then he again turned around 7 minutes hourglass which had counted 4 minutes. That's how 7 minutes counted 4 minutes again.

5. In this way, 11 + 4 = 15 minutes counted.

Cars Across the Desert

A military car carrying an important letter must cross a desert. 

There is no petrol station on the desert and the car has space only for petrol that lasts to the middle of the desert.

There are also other cars that can transfer their petrol into one another.

How can the letter be delivered?

Delevering letter across the desert

This is how letter can be delivered!

Delivering Letter Across The Desert

What was the task?

We need 4 such cars to deliver the letter across the desert successfully.

Let's divide the entire route into 6 parts. That means the distance that car can travel (half the total path in desert) is divided into 3 parts. To travel each part car requires 1/3rd of it's petrol in the tank.

1. At first 1/6th of total path, all cars are 2/3rd full. Now 2/3rd of the petrol from 1 car can be used to fill 1/3rd of tanks in other 2 cars (1/3 + 1/3 = 2/3). This way, we would have 2 cars full while 1 car 2/3rd full. We are leaving behind the empty car, taking 3 cars forward.

Journey of Letter Across The Desert
Stage 1

2. At next 1/6th of the distance, 2 full cars will use 1/3rd of their petrol hence would be 2/3rd full. And the car that was 2/3rd at previous stage would be not 1/3rd full. At this stage, the petrol from car that is 1/3rd full can be used to fill tank of 1 car completely. So we are leaving behind one another empty car here & taking fully filled car & 2/3rd filled car for next stage.

Journey of Letter Across The Desert
Stage 2

3. For next 1/6th of the total distance, the car that was fully filled would have 2/3rd petrol. And the car which was 2/3rd at previous stage would be now 1/3rd filled. The petrol of this car can be used to fill the tank of the first car. Now we have 1 car fully filled while other one is empty. So we can leave behind the empty car & use fully filled car for the rest half of the journey. Remember, a car which tank is full can travel half the total path.

Journey of Letter Across The Desert
Stage 3

Monday, January 1, 2018

Who Works Where?

Alex, Betty, Carol, Dan, Earl, Fay, George and Harry are eight employees of an organization
They work in three departments: Personnel, Administration and Marketing with not more than three of them in any department.

Each of them has a different choice of sports from Football, Cricket, Volleyball, Badminton, Lawn Tennis, Basketball, Hockey and Table Tennis not necessarily in the same order.

1.Dan works in Administration and does not like either Football or Cricket.

2.Fay works in Personnel with only Alex who likes Table Tennis.

3.Earl and Harry do not work in the same department as Dan.

4.Carol likes Hockey and does not work in Marketing.

5.George does not work in Administration and does not like either Cricket or Badminton.

6.One of those who work in Administration likes Football.

7.The one who likes Volleyball works in Personnel.

8.None of those who work in Administration likes either Badminton or Lawn Tennis.

9.Harry does not like Cricket.

Find the department & Favorite sport of each employee.
Who are the employees who work in the Administration Department?

In which Department does Earl work?

Click here for the complete picture. 

Employees of Each Department

What was the data given? 

Let's make a table where columns represent the sport & row represents the employee.There are 3 tables 1 for each department. To make table shorter we will use the initials only of sports' & employees' names as below.

Possible Deparment & Favorite Sport of Each Employee

A - Alex, B - Betty, C - Carol, D - Dan, E - Earl, F - Fay, G - George, H - Harry. 

F - Football, C - Cricket, V - Volleyball, Bd - Badminton, LT - Lawn Tennis, Bs - Basketball,
H - Hockey, TT - Table Tennis  

Now taking clues one by one into consideration.

1. Dan works in Administration and does not like either Football or Cricket.

Possible Deparment & Favorite Sport of Each Employee
Table 1

2. Fay works in Personnel with only Alex who likes Table Tennis.

This indicates that Alex is working in Personnel department & likes Table Tennis. Fay working in same department may like any other sports than Table Tennis. No body other working in this department.

Possible Deparment & Favorite Sport of Each Employee
Table 2
3. Earl and Harry do not work in the same department as Dan.

Hence they must be working in Marketing department!

Possible Deparment & Favorite Sport of Each Employee
Table 3
4. Carol likes Hockey and does not work in Marketing.

That's why his department must be Administration.

Possible Deparment & Favorite Sport of Each Employee
Table 4
5. George does not work in Administration and does not like either Cricket or Badminton.

His department must be Marketing & he might be liking Football or Volleyball or Lawn Tennis or Basketball.

Possible Deparment & Favorite Sport of Each Employee
Table 5