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Problem #6
A salesman's commission is 5% on all sales up to $10,000 and 4% on all sales exceeding this. He remits $31,100 to his parent company after deducting his commission. His sales was worth $_________.
Mr. Black, Mr. Gray, and Mr. White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr. Black, who hits his shot 1/3 of the time, gets to shoot first. Mr. Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr. White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr. Black, where should you shoot first for the highest chance of survival? ![]()
Reminded me of an old joke:-
The European Union commissioners have announced that agreement has been reached to adopt English as the preferred language for European communications, rather than German, which was the other possibility.
As part of the negotiations, Her Majesty's Government conceded that English spelling had some room for improvement and has accepted a five-year phased plan for what will be known as EuroEnglish (Euro for short).
In the first year, 's' will be used instead of the soft 'c'. Sertainly, sivil servants will resieve this news with joy. Also, the hard 'c' will be replaced with 'k.' Not only will this klear up konfusion, but typewriters kan have one less letter.
There will be growing publik enthusiasm in the sekond year, when the troublesome 'ph' will be replaced by 'f'. This will make words like 'fotograf' 20 per sent shorter.
In the third year, publik akseptanse of the new spelling kan be expekted to reach the stage where more komplikated changes are possible. Governments will enkourage the removal of double letters, which have always ben a deterent to akurate speling. Also, al wil agre that the horible mes of silent 'e's in the languag is disgrasful, and they would go.
By the fourth year, peopl wil be reseptiv to steps such as replasing 'th' by 'z' and 'w' by 'v'.
During ze fifz year, ze unesesary 'o' kan be dropd from vords kontaining 'ou', and similar changes vud of kors; be aplid to ozer kombinations of leters.
After zis fifz yer, ve vil hav a reli sensibl riten styl. Zer vil b no mor trubls or difikultis and evrivun vil find it ezi tu understand ech ozer. Ze drem vil finali kum tru. ![]()
You'd kill me for telling this, but the solution is
that he was born in a hospital in room No.1975
and he died in a hospital in room No.1995.
I never said those were the years, did I? ![]()
You got it √
A cistern can be filled by two pipes A and B separately in 45 minutes and 36 minutes respectively. A tap C at the bottom can empty the cistern in 30 minutes. If the tap C is opened 7 minutes after the two pipes A and B are opened, in how many minutes will the cistern be full?
A person was born in 1975 and he died in 1995. He was 25 years of age when he died. How?
(This one's a lateral thinking puzzle
)
1 20 19
2 19 17
3 18 15
4 17 13
5 16 11
6 15 9
7 14 7
8 13 5
9 12 3
10 11 1
That's 100!
Re-arranging,
1 17 16
2 20 18
3 13 10
4 19 15
5 16 11
6 18 12
7 15 8
8 14 6
9 11 2
10 12 2
100 yet again!
Should it be always (n/2)² for 0 to n??? ![]()
(Just like the side total of a magic square containing numbers 1 to n² is
(n³+n)/2 ???
)
I once knew someone named justlooking,
Who had a knack for hookin'
Everytime he tried his skill
I um unable to reply. I shall wait for your post and comment on that later, MathsIsFun.
#4 (Without paper, pencil; Time limit : 1 minute)
The sum of three numbers is 174. The ratio of the second number to the third is 9:16 and the ratio of the first number to the third is 1:4. The second number is _______.
Since both the ratios have 4 or a multiple of 4 for C,
the ratio A:B:C = 4:9:16.
The sum of these is 29, and it can be noticed 174 is 29 x 6.
Therefore, the second number is 9 x 6, that is 54.
Ist truck:- 3 full cylinders, 1 half-full and 3 empty
IInd truck:- 2 full cylinders, 3 half-full and 2 empty
IIIrd truck:- 2 full cylinders, 3 half-full and 2 empty
PS:- The Moderator may remove my reply if he/she wants it to be left open.
You are right, Mathsy! ![]()
#4 (Without paper, pencil; Time limit : 1 minute)
The sum of three numbers is 174. The ratio of the second number to the third is 9:16 and the ratio of the first number to the third is 1:4. The second number is _______.
Jenilia, we shall prepare you for the Olympiad;
I shall start with my first lesson,
do you know how recurring decimals are converted into fractions?
Lets assume x=0.1414141414....................
100 x = 14.14141414.....................
Deducting equation (2) from (1),
99x = 14
x = 14/99
Mathsy, you are, I repeat, you are, really smart! ![]()
I saw this problem and I was impressed. I didn't know someone had posted a similiar problem earlier. Okay, I shall give the solution and post a new problem instead.
The solution :- 6 /(1-3/4)
The new problem #3
Imagine you are writing numbers from 1 to 1000 on a piece of paper. How many times would you write the number'9'? ![]()
tt is, relatively, a newcomer, and he /she solves my problems quickly. ![]()
I had requested this member to wait for the others to post their replies, maybe he/she thought this was unanswered for quite some time. ![]()
I shall try to solve that when I start the next week,
here's my problem for the day ![]()
Using the numbers 1, 3, 4, and 6, together with the operations +, -, ×, and ÷, and unlimited use of brackets, make the number 24. Each number must be used precisely once. Each operation may be used zero or more times. Decimal points are not allowed, nor is implicit use of base 10 by concatenating digits, as in 64 - 31.
I am unable to guess why she did it!
I am jumping in! ![]()
You are correct, tt! ![]()
Thats right!
This is how it is solved.
40 litres of milk and water contain 10% water.
Therefore, the milk content is 36 litres and water is 4 litres.
Lets assume x litres of water are added to make water 20%.
The ratio of water to the total becomes
4+x/40+x
this is equal to 20/100 or 1/5.
4+x/40+x = 1/5,
5(4+x) = 40+x
20+5x = 40+x
4x=20
x=5 litres
Don't hate Mathematics, Zoe! Mathematics is fun, believe me! ![]()
I wonder if ganesh would like to play?
I am too old...I am more than 10,000 days old! ![]()
That is close to a 1,000 gallons!
who looked much like a lizard