(Puzzles) Challenging Mathematical Puzzles (36)

Puzzles : Challenging Mathematical Puzzles

123. Dr. DoLittle always goes walking to the clinic and takes the same time while going and while coming back. One day he noticed something.
When he left the home, the hour hand and the minute hand were exactly opposite to each other and when he reached the clinic, they were together.
Similarly, when he left the clinic, the hour hand and the minute hand were together and when he reached the home, they were exactly opposite to each other.
How much time does Dr. DoLittle take to reach home from the clinic? Give the minimal possible answer.

Answer : -
32 minutes 43.6 seconds

In twelve hours, the minute hand and the hour hand are together for 11 times. It means that after every 12/11 hours, both the hands are together.

Similarly in twelve hours, the minute hand and the hour hand are exactly opposite to each other for 11 times. It means that after every 12/11 hours, both the hands are opposite.

Now, let's take an example. We know that at 12 both the hands are together and at 6 both the hands are exactly opposite to each other.

After 6, both the hands are in opposition at [6+(12/11)] hours, [6+2*(12/11)] hours, [6+3*(12/11)] hours and so on. The sixth such time is [6+6*(12/11)] hours which is the first time after 12. Thus after 12, both the hands are opposite to each other at 12:32:43.6

Hence, Dr. DoLittle takes 32 minutes and 43.6 seconds to reach home from the clinic. 

 

124. SlowRun Express runs between Bangalore and Mumbai, For the up as well as the down journey, the train leaves the starting station at 10:00 PM everyday and reaches the destination at 11:30 PM after three days.
Mr. Haani once traveled by SlowRun Express from Mumbai to Bangalore. How many SlowRun Express did he cross during his journey?

Answer : -
Mr. Haani crossed 7 SlowRun Expresses during his journey.

Let's say that Mr. Haani travelled by SlowRun Express on Wednesday 10:00PM from Mumbai. The first train he would have crossed is the one scheduled to arrive at Mumbai at 11:30 PM the same day i.e. the one that left Bangalore at 10:00 PM on last Sunday.

Also, he would have crossed the last train just before reaching Bangalore on Saturday.

Thus, Mr. Haani must have crossed 7 SlowRun Expresses during his journey.

 

125. Six cabins numbered 1-6 consecutively, are arranged in a row and are separated by thin dividers. These cabins must be assigned to six staff members based on following facts.
    1. Miss Shalaka's work requires her to speak on the phone frequently throughout the day.
    2. Miss Shudha prefers cabin number 5 as 5 is her lucky number.
    3. Mr. Shaan and Mr. Sharma often talk to each other during their work and prefers to have adjacent cabins.
    4. Mr. Sinha, Mr. Shaan and Mr. Solanki all smoke. Miss Shudha is allergic to smoke and must have non-smokers adjacent to her.
    5. Mr. Solanki needs silence during work.

Can you tell the cabin numbers of each of them?

Answer : -
The cabins from left to right (1-6) are of Mr. Solanki, Mr. Sinha, Mr. Shaan, Mr. Sharma, Miss Shudha and Miss Shalaka.

From (2), cabin number 5 is assigned to Miss Shudha.

As Miss Shudha is allergic to smoke and Mr. Sinha, Mr. Shaan & Mr. Solanki all smoke, they must be in cabin numbers 1, 2 and 3 not necessarily in the same order. Also, Miss Shalaka and Mr. Sharma must be in cabin 4 and 6.

From (3), Mr. Shaan must be in cabin 3 and Mr. Sharma must be in cabin 4. Thus, Miss Shalaka is in cabin 6.

As Mr. Solanki needs silence during work and Mr. Shaan is in cabin 3 who often talks to Mr. Sharma during work, Mr. Solanki must be in cabin 1. Hence, Mr. Sinha is in cabin 2.

Thus, the cabins numbers are : -
1 Mr. Solanki,
2 Mr. Sinha,
3 Mr. Shaan,
4 Mr. Sharma,
5 Miss Shudha,
6 Miss Shalaka

 

126. SkyFi city is served by 6 subway lines - A, E, I, O, U and Z.
    When it snows, morning service on line E is delayed.
    When it rains or snows, service on the lines A, U and Z is delayed both morning and afternoon.
    When the temperature drops below 20 C, afternoon service is cancelled on either line A or line O, but not both.
    When the temperature rises above 40 C, afternoon service is cancelled on either line I or line Z, but not both.
    When service on line A is delayed or cancelled, service on line I is also delayed.
    When service on line Z is delayed or cancelled, service on line E is also delayed.

On February 10, it snows all day with the temperature at 18C. On how many lines service will be delayed or cancelled, including both morning and afternoon?

SkyFi city is served by 6 subway lines - A, E, I, O, U and Z.

* When it snows, morning service on line E is delayed.
* When it rains or snows, service on the lines A, U and Z is delayed both morning and afternoon.
* When the temperature drops below 20 C, afternoon service is cancelled on either line A or line O, but not both.
* When the temperature rises above 40 C, afternoon service is cancelled on either line I or line Z, but not both.
* When service on line A is delayed or cancelled, service on line I is also delayed.
* When service on line Z is delayed or cancelled, service on line E is also delayed.

On February 10, it snows all day with the temperature at 18C. On how many lines service will be delayed or cancelled, including both morning and afternoon?

In a certain game, if 2 wixsomes are worth 3 changs, and 4 changs are worth 1 plut, then 6 plutes are worth how many wixsomes?

Answer : - 
It is given that
2 wixsomes = 3 changs
8 wixsomes = 12 changs ----- (I)

Also, given that
4 changs = 1 plut
12 changs = 3 plutes
8 wixsomes = 3 plutes ----- From (I)

Therefore,
6 plutes = 16 wixsomes

 

127. In a certain year, the number of girls who graduated from City High School was twice the number of boys. If 3/4 of the girls and 5/6 of the boys went to college immediately after graduation, what fraction of the graduates that year went to college immediately after graduation?

Answer : - 
Assume that number of boys graduated from City High School = B
Therefore, number of girls graduated from City High School = 2*B

It is given that 3/4 of the girls and 5/6 of the boys went to college immediately after graduation.
Hence, total students went to college
= (3/4)(2*B) + (5/6)(B)
= B * (3/2 + 5/6)
= (7/3)B

Fraction of the graduates that year went to college immediately after graduation
= [(7/3)B] / [3*B]
= 7/9

Therefore, the answer is 7/9

 

128. A mule and a donkey were carrying full sacks on their backs.
The mule started complaining that his load was too heavy. The donkey said to him "Why are you complaining? If you gave me one of your sacks I'd have double what you have and if I give you one of my sacks we'd have an even amount."
How many sacks were each of them carrying? Give the minimal possible answer.

Answer : - 
 
The mule was carrying 5 sacks and the donkey was carrying 7 sacks.
Let's assume that the mule was carrying M sacks and the donkey was carrying D sacks.

As the donkey told the mule, "If you gave me one of your sacks I'd have double what you have."
D + 1 = 2 * (M-1)
D + 1 = 2M - 2
D = 2M - 3

The donkey also said, "If I give you one of my sacks we'd have an even amount."
D - 1 = M + 1
D = M + 2

Comparing both the equations,
2M - 3 = M + 2
M = 5

Substituting M=5 in any of above equation, we get D=7

Hence, the mule was carrying 5 sacks and the donkey was carrying 7 sacks.

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