Below, you will find the mathematical proof that 10 equals 9.99999…. But is that possible or there is something wrong about it? Can you find the error?
x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10
No error is present in this proof and 10 is actually equal to 9.99999…. The proof is absolutely correct.
You have $100 with you and you have to buy 100 balls with it. 100 is the exact figure and you cant go below or above the numbers and you have to use the entire $100. If there is no kind of tax applied how many of each of the following balls will you be able to buy:
Green Balls costing $6
Yellow Balls costing $3
Black Balls costing $0.10
Now, how many of each must you buy to fulfill the condition given?
1 green ball = $6
29 yellow balls = $87
70 black balls = $7
Detailed Explanation :
Let us denote the number of balls to be brought with a variable
p = green sponges
q = yellow sponges
r = black sponges
Now using a simple expression:
p + q + r = 100
6p + 3q + 0.1r = 100
Multiplying the first equation by 6 then 3 and subtracting the two equations, we get:
6p + 6q + 6r = 600
3p + 3q + 3r = 300
3q = 500 - 5.9r
3p = 2.9r - 200
Usually, we have three equations to solve three variables. However, we will manage with just two here because we know that p and q are non-negative integers.
If 3q >/= 0, then 500 - 5.9r >/= 0.
Using this, r
Also, if 3p >/= 0, then 2.9r - 200 > 0. This implies that r >/= 68.97.
Now, the number of black balls must be an even dollar amount or we will land up with a fraction. Considering the expressions, you know that there can be just two integers that can satisfy the condition while lying in between 68.97 and 84.75.
If we take r as 80 and solve the equations (the last two equations), we will get p = 10.67 and q = 9.33. But p and q must be integer and not fraction. Thus you can cancel out 80.
If we take r as 70, we will get p = 1 and b = 29.
Therefore following are the number of balls that we must buy:
1 green ball = $6
29 yellow balls = $87
70 black balls = $7
A man is approaching a broad and barren land. He has a package with him. If somehow, he is unable to open the package before reaching the land, he will die.
Can you guess what is present in the package?
The package contains a parachute and he has doing air diving.
An equation has been laid down using a few matchsticks. However, as you can see, the equation is not correct. Can you correct the equation if you are allowed to add or remove 5 matchsticks?
As you can see in the answer figure, the equation stands true now. Compare the images to know what we have done.
A Japanese ship was en route to a mission in foreign seas. The captain of the ship felt tired and thought of taking a bath. He went for taking the shower and removed his diamond ring and Rolex and kept them on the table. When he returned after taking the bath, he found that the ring and watch were stolen.
He called the five members of the crew whom he suspected and asked them what they were doing for the last 15 minutes.
The Italian cook (with a butcher knife in hand): I was in fridge room getting meat for cooking.
The British Engineer (with a high beam torch in hand): I was working on generator engine.
The Pakistani seaman: I was on the mast correcting the flag which was upside down by mistake.
The Indian Radio officer: I was trying to make a contact with the company to inform them about our position.
The American navigation officer: I am on night watch, so I was sleeping in my cabin.
Upon listening to them, the captain caught the lying member. Who do you think stole the valuables?
The Pakistani seaman is lying. This is because the Japanese flag looks the same upside down. There was no need to correct it and thus he is plainly lying.
A guy was writing his first book. After saving the document, he locked his laptop with a password and mentioned some phrases for the hint box.
A friend of his tried opening his laptop but found out that it was password protected. Following is the hint that appeared.
1 mobile 3 books 2 roars 1 night 4 balls 2 lighters 1 ghost 1 hat 3 watches
It seemed awkward to him. Can you help him in cracking the password?
The password is - Moonlight
If you are wondering how, then the answer lies in the hint only. You have to take the corresponding number letter of each word.
1st in mobile is M
3rd in books is O
2nd in roars is O
1st in night is N
4th is balls is L
2nd in lighters is I
1st in ghost is G
1st in hat is H
3rd in watches is T.
I engaged in a strange activity. My birthday was approaching and I decided to collect money for my birthday bash. On the first day of the month, I kept a dollar in my piggy bank, on the second, I kept two dollars and on the third, I kept three and so on.
On my birthday, I had a total of 276 dollars in my piggy bank. Can you find out on which day of the month was my birthday?
23rd
The easiest way to find out without engaging in any formula would be to simply add them:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 = 276
Thus, the birthday falls on the 23rd day of the month.
In the given picture, you can find five identical squares. You have to form six identical squares by moving just three matchsticks. How will you achieve it if you are not allowed overlapping or breaking of matchsticks?
As you can see in the picture, we have lifted the bottom three matches and placed them inside the middle squares vertically (pink ones). We now have six identical squares.
This black and white picture shows a couple by the lakeside. The picture is quite serene. But can you find out something in this picture that does not meet the eyes?
If you would have concentrated over the branches of the tree, you would have found out. It is a baby face. We have highlighted the picture for you.
Below, you can see some coding:
January = 1017
February = 628
March = 1335
April = 145
May = 1353
June = 1064
July = 1074
August = 186
Now deciphering the way it has been coded, can you find out how September will be coded?
January = 10|1|7
10 is the position of letter J in alphabetical order.
1 is the position of January in months.
7 is the number of letters used in the word January.
Same goes for all the months, thus
September = 19|9|9 (1999).