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Twenty men, women and children earn twenty coins between them. Each man earns 3 coins, each woman 1.5 coins and each child 0.5 coin.
How many men, women and children are there?
Find number of each of them here!
What was the question?
Let's suppose there are m men, w women and c children.
As per given data,
m + w + c = 20 ......(1)
3m + 1.5w + 0.5c = 20 .....(2)
Multiply equation (1) by 3 and then subtracting from (2), we get,
5m + 2w = 20.
For m and w to be whole numbers, m must be 2 and w must be 5 satisfying above equation.
Hence, from (1),
c = 20 - 2 - 5 = 13.
To conclude, there are 2 men, 5 women and 13 children.
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!
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.
Someone drove from Aardvark to Beeville.
On the first, day they traveled 1/3 of the distance.
On day two, they traveled 1/2 of the remaining distance.
On day three, they traveled 2/3 of the remaining distance.
On day four, after covering 3/4 of the remaining distance, they were still 5 miles away from Beeville.
How many miles had they covered so far?
Know the total distance traveled!
Click for the question!
We need to start in reverse.
In last part after covering 3/4 still 5 miles left which accounts for 1/4 of remaining distance. Hence, 20 miles were left at the start of DAY 4.
On DAY 3, 2/3rd covered leaving 20 miles for DAY 4. That means 20 miles distance is remaining 1/3rd. Hence, at the start of DAY 3, 60 miles were left.
On DAY 2, 1/2 of covered leaving 60 miles for DAY 2. So that means 60 miles distance is remaining 1/2. So at the start of DAY 2, 120 miles yet to be covered.
On DAY 1, 1/3 of covered leaving 120 miles for DAY 2. Meaning 120 miles distance is remaining 2/3. Hence, 180 miles yet to be covered at the start of DAY 1.
Out of 180 miles, 175 covered in 4 days still 5 miles left.
Six people park their car in an underground parking of a store.
The store has six floors in all. Each one of them goes to different floor.
Simon stays in the lift for the longest.
Sia gets out before Peter but after Tracy.
The first one to get out is Harold.
Debra leaves after Tracy who gets out at the third floor.
Can you find out who leaves the lift at which floor?
Was it really so difficult?
What was the given data?
The sentence 'The first one to get out is Harold.' suggests that the Harold leaves the lift at the 1st floor.
Similarly, the sentence - 'Simon stays in the lift for the longest.' suggests that Simon leaves he lift at the 6th floor.
Next, sentence - 'Debra leaves after Tracy who gets out at the third floor' suggests Debra leaves the lift at the 3rd floor.
Clearly, the sentence - 'Sia gets out before Peter but after Tracy.' suggests that Sia leaves the lift at the 4th floor.
Also, it is clear that Debra leaves the lift at the 2nd floor and Peter at the 5th floor.
Summary -
Harold leaves at the first floor.
Debra leaves at the second floor.
Tracy leaves at the third floor.
Sia leaves at the fourth floor.
Peter leaves at the fifth floor.
Simon leaves at the sixth floor.
Bob buys two things in a shop. With his pocket calculator he calculates in advance what he has to pay: 5.25 dollars. But what he does not notice is that he pressed the division instead of the addition button. At the desk he is not surprised if he hears that he has to pay 5.25 dollars.
What is the price of the two things Bob has bought?
Know the cost of those 2 things.
What was the mistake?
Let's assume that those things costs a and b respectively.
As per Bob's wrong calculation,
a / b = 5.25
a = 5.25 b ..........(1)
And according to what should have been correct,
a + b = 5.25
Putting (1) in above,
5.25b + b = 5.25
6.25b = 5.25
b = 0.84
Again putting this value in (1) gives,
a + 0.84 = 5.25
a = 5.25 - 0.84
a = 4.41
Hence the cost of 2 things are $4.41 and $0.84.
In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly.
How many people have guessed three fruits correctly, and how many people have guessed four fruits correctly?
Escape to answer without getting tricked!
What was the game?
There is absolutely no way that somebody has guessed 3 correctly since if 3 are correct then 4th has to be correct. Hence, nobody guessed 3 correctly.
So number of people with all 4 guess correct is equal to 123 - 43 - 39 - 31 = 10.
10 people guessed all the 4 fruits correctly.
A rich merchant had collected many gold coins. He did not want anybody to know about them.
One day, his wife asked, “How many gold coins do we have?”
After pausing a moment, he replied, “Well! If I divide the coins into two unequal numbers, then 32 times the difference between the two numbers equals the difference between the squares of the two numbers.”
The wife looked puzzled. Can you help the merchant’s wife by finding out how many gold coins they have?
Here are mathematical steps to find those!
What was that clue?
Since when divided into 2 unequal numbers difference won't be 0. Let x and y be the 2 unequal numbers.
As per merchant,
32 (x - y) = x^2 - y^2
32 (x - y) = (x - y) (x + y)
Dividing both sides by (x - y) which is non zero as x is not equal to y,
32 = x + y
x + y = 32.
Let's verify with x = 30 and y = 2. So 32 (x - y) = 32 ( 30 - 2) = 896. And x^2 - y^2 = 30^2 - 2^2 = 900 - 4 = 896.
Hence, Merchant had 32 coins in total.
Whether it’s possible to construct a magic square using the first nine prime numbers (here counting 1 as prime):
1 2 3 5 7 11 13 17 19
Is it?
Find the possibility here!
What was the task given?
That's impossible task. All the listed prime numbers sums together to 78. For square to be magic, sum of each row & column must be equal. In this case, it should be 78/3 = 26.
For sum of 3 to be even, 1 must be even & other 2 odd (or all even). All 3 odd can't sum even.
In listed prime numbers there is only 1 even number i.e.2. Hence, for other 2 rows/columns we can't have even sum.
There is an Island of puzzles where numbers 1 - 9 want to cross the river.
There is a single boat that can take numbers from one side to the other.
However, maximum 3 numbers can go at a time and of course, the boat cannot sail on its own so one number must come back after reaching to another side.
Also, the sum of numbers crossing at a time must be a square number.
You need to plan trips such that minimum trips are needed.
This should be that minimum number!
What was the challenge?
We need only 7 trips to send all digits across the river.
1. Send 2, 5, 9 (sum is 16).
2. Bring back the 9.
3. Send 3,4, 9 (sum is 16).
4. Bring back the 9.
5. Now send 1,7,8 (sum is 16).
6. Bring back the 1.
7. And finally send 1,6,9 (sum is 16).
A prisoner is faced with a decision where he must open one of two doors. Behind each door is either a lady or a tiger. They may be both tigers, both ladies or one of each.
If the prisoner opens a door to find a lady he will marry her and if he opens a door to find a tiger he will be eaten alive. Of course, the prisoner would prefer to be married than eaten alive :).
Each of the doors has a statement written on it. The statement on door one says, “In this room there is a lady, and in the other room there is a tiger.”
The statement on door two says, “In one of these rooms there is a lady, and in one of these rooms there is a tiger.”
The prisoner is informed that one of the statements is true and one is false.
Which door should the Prisoner open?
This should be his choice!
What were the choices?
For a moment, let's assume that first statement is true. The lady is behind the Door 1 and tiger is behind the Door 2. But this makes statement 2 also true where it says there is tiger behind one of these door & lady behind one of these doors. Hence, the statement 1 can't be true.
Hence, statement 2 must be true.
Only possibilities left are -
Door 1 - Tiger
Door 2 - Tiger
Door 1 - Lady
Door 2 - Lady
Door 1 - Tiger
Door 2 - Lady.
Since, the true second statement is suggesting there is lady behind 1 & tiger behind the other door, the possibilities of both tigers or ladies are eliminated.
That's why behind Door 1 is tiger & behind Door 2 is lady.
