Brain Teasers

BT1:

At what time immediately prior to Six O'clock the hands of the clock are exactly opposite to each other.
Give the exact time in hours, minutes and seconds.

Answer
4 hrs. 54 min. 32.74 seconds

How to find it???
It is obvious that between 5 O'clock and 6 O'clock the hands will not be exactly opposite to each other. It is also obvious that
the hands will be opposite to each other just before 5 O'clock. Now to find exact time:
The hour hand moves 1 degree for every 12 degrees that the minute hand moves. Let the hour hand be X degree away from 5
O'clock. Therefore the minute hand is 12X degree away from 12 O'clock.
Therefore solving for X
Angle between minute hand and 12 O'clock + Angle between 12 O'clock and 4 O'clock + Angle between 4 O'clock and hour
hand = 180
12X + 120 + (30-X) = 180
11X = 30
Hence X = 30/11 degrees
(hour hand is X degree away from 5 O'clock)
Now each degree the hour hand moves is 2 minutes.
Therefore minutes are
= 2 * 30/11
= 60/11
= 5.45 (means 5 minutes 27.16 seconds)
Therefore the exact time at which the hands are opposite to each other is
= 4 hrs. 54 min. 32.74 seconds!

BT2:

Ali Baba had four sons, to whom he bequeathed his 39 camels, with the proviso that the legacy be divided in the following way :
The oldest son was to receive one half the property, the next a quarter, the third an eighth and the youngest one tenth. The four
brothers were at a loss as how to divide the inheritance among them without cutting up a camel, until a stranger appeared
upon the scene.
Dismounting from his camel, he asked if he might help, for he knew just what to do. The brothers gratefully accepted his offer.
Adding his own camel to Ali Baba's 39, he divided the 40 as per the will. The oldest son received 20, the next 10, the third 5 and
the youngest 4. One camel remained: this was his, which he mounted and rode away.
Scratching their heads in amazement, they started calculating. The oldest thought: Are not 20 greater than the half of 39? Someone
must have received less than his proper share! But each brother discovered that he had received more than his due. How is it possible?

Answer
they took their percentages from 40 and not from 39, so they got more than their share.
The oldest son got 1/2 of 40 = 20 which is 0.5 more
The second son got 1/4 of 40 = 10 which is 0.25 more
The third son got 1/8 of 40 = 5 which is 0.125 more
The youngest son got 1/10 of 40 = 4 which is 0.1 more
And the stranger got 1/40 of 40 = 1 which is 0.025 more (As he is not supposed to get anything)
All these fractions add to = 0.5 + 0.25 + 0.125 + 0.1 + 0.025 = 1 which stranger took away.

BT3:

In a hotel, rooms are numbered from 101 to 550. A room is chosen at random. What is the probability that room number starts with
1, 2 or 3 and ends with 4, 5 or 6?

Answer:
There are total 450 rooms.
Out of which 299 room number starts with 1, 2 or 3. (As room number 100 is not there) Now out of those 299 rooms only
90 room numbers end with 4, 5 or 6
So the probability is 90/450 i.e. 1/5 or 0.20

BT4:

A man went into a fast food restaurant and ate a meal costing Rs. 105, giving the accountant a Rs. 500 note. He kept the change, came back a few minutes later and had some food packed for his girl friend. He gave the accountant a Rs. 100 note and received Rs. 20 in change. Later the bank told the accountant that both the Rs. 500 and the Rs. 100 notes were counterfeit.
How much money did the restaurant lose? Ignore the profit of the food restaurant.

Answer
He lost Rs.600
First time restaurant has given food worth Rs.105 and Rs. 395 change. Similarly second time, food worth Rs.80 and Rs.20 change. Here, we are not considering food restaurant profits.

BT5:

You are working in a store that stocks bangles. Three boxes of bangles have been incorrectly labeled. The labels say Red Bangles,
Green Bangles and Red & Green Bangles.
How can you re-label the boxes correctly, by taking only one bangle from one box?

Answer
Keep in mind that boxes are incorrectly labeled.
Take out one bangle from the box labeled "Red & Green Bangles". There are 2 possibilities:
If that bangle is Red, it means that box contains Red Bangles. The box labeled as "Green Bangles" contains Red & Green
Bangles. And box labeled "Red Bangles" contains Green bangles.
RED GREEN BOX --- Red Bangles
RED BOX --- Green Bangles
GREEN BOX --- Red & Green Bangles
If that bangle is Green, it means that box contains Green
Bangles. The box labeled as "Green Bangles" contains Red
Bangles. And box labeled "Red Bangles" contains Red &
Green Bangles.
RED GREEN BOX --- Green Bangles
RED BOX --- Red & Green Bangles
GREEN BOX --- Red Bangles

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