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Maths Puzzle
The hour and minute hands are at equal distance from the 6 hour, what time will it be exactly?
Read Solution (Total 1)
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Say answer is "8 hour X minute". According as proposition, the angle between the minute hand and "mark 4" of the watch is equal to the angle between the hour hand and "mark 8" of the watch.
We know in 60 minutes the minute hand makes 360 degrees (360/60=6 degrees per minute) and the hour hand makes 360/12=30 degrees (30/60=1/2 degrees per minute).
Therefore, (20-X) minutes corresponds to 6(20-X) degrees (this is the angle between the minute hand and "mark 4").
And in X minutes the hour hand makes X/2 degrees with "mark 8".
Thus, X/2=6(20-X) gives X=18 minutes 27 and 9/13 second.
So, the answer is 8 hour, 18 minutes, 27 9/13 second.
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self Other Question
On your travels you come to an old man on the side of the road holding three cards from a standard deck face down. Trying to make conversation you ask him what the three cards are.
He tells you, "To the left of the queen, are one or two jacks. To the right of the jack, are one or two jacks. To the right of the club, are one or two diamonds. To the left of the diamond, are one or two diamonds." What are the three cards?
Here is a puzzle known as the Covent Garden Problem, which appeared in London half a century ago, accompanied by the somewhat surprising assertion that it had mystified the best mathematicians of England:
Mrs. Smith and Mrs. Jones had equal number of apples but Mrs. Jones had larger fruits and was selling hers at the rate of two for a penny, while Mrs. Smith sold three of hers for a penny.
Mrs. Smith was for some reason called away and asked Mrs. Jones to dispose of her stock. Upon accepting the responsibility of disposing her friend's stock, Mrs. Jones mixed them together and sold them of at the rate of five apples for two pence.
When Mrs. Smith returned the next day the apples had all been disposed of, but when they came to divide the proceeds they found that they were just seven pence short, and it is this shortage in the apple or financial market which has disturbed the mathematical equilibrium for such a long period.
Supposing that they divided the money equally, each taking one-half, the problem is to tell just how much money Mrs. Jones lost by the unfortunate partnership?