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Wednesday, 31 December 2014

Tell the Time

 Can you tell at what time between 7 and 8 O’ clock, the two hands of a clock, will be in a straight line?

Answer:  5-5 / 11 minutes, past 7.

Exactly at 7 O’ clock the minute hand is 35 divisions behind the hour hand. In order to be opposite one another the minute hand must gain 5 divisions on the hour hand.

However, the minute hand gains 35 divisions in 60 true minutes.

 And therefore the minute hand gains 5 divisions in 5-5 / 11 true minutes.


How much is a googolplex?

Answer: 1 googolplex = 10 googol = 1 followed by a googol of zeroes = 100 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 00

A Problem of Drinks

              I love to mix drinks. When I have one glass orangeade and one glass lemonade each glass contains the same amount. I take 2 ounces full of the orangeade and mix it with the lemonade, and then I take 2 ounces full of this mixture and put it back in the orangeade. What do you think of the resulting mixture?
             Do you think there is more orangeade in the lemonade or more lemonade in the orangeade?

Answer:  Neither. There is same amount in each. Let us assume:

A= amount of orangeade in glass at start
B= amount of orangeade first transferred.
      C= amount of orangeade transferred second time
D= amount of Lemonade transferred to orangeade
Now we must show that the amount of Lemonade in orangeade equals the amount of orangeade in the Lemonade or, in terms of a ,b, c, d we must show that:
D= b –c

 Time                                                Amount of Orangeade in Glass
Start                                                                      a
1st Transfer                                                         a – b
2nd Transfer                                                (a-b) + (c + d)

The starting amount, a, must equal the final amount after the second transfer.
A= (a-b) + c +c d or d = b - c  

The Spoilt Holiday

            A group of friends and me went on a holiday to a hill station. It rained for 13 days. But when it rained in the morning the afternoon was lovely. And when it rained in the afternoon the day was preceded by a clear morning.
          Altogether there were 11 very nice mornings and 12 very nice afternoons. How many days did our holiday last?

Answer: Our holiday lasted for 18 days. First of all let us see how many possible types of days there could be. There could only be three such as: 

             Rain in the morning and fine in the afternoon 
       Fine in the morning and fine in the afternoon 
           Fine in the morning and rain in the afternoon

Let us assume the number of such days in each category be a, b and c.
Then: Number of days on which rain falls = a + c = 13
Number of days with fine mornings = b +c = 11
Number of days with fine afternoons = a + b = 12
We derive from these equations that:

A=7,   b = 5, c = 6
 Therefore the number of days on holiday is:
 7+ 5+ 6 + 18

Make a Sequence

      What are the next two terms of the sequence?
1, 1, 5, 17, 61,217………………

Answer:   773, 2753: In this sequence we have to try all the combinations of mathematical operations we know until we find the order which satisfies the sequence. The order in this case is:
Tn= 3 Tn- 1 + 2 Tn -2
T₇ = 3x 217 + 2 x 61 = 773

Weight of Diamonds

   What is the measure used to weigh diamonds?

Answer: Carat. Carat is the standard legal weight for the sale of Diamonds, precious stones and precious metals, since 1878.
              A Carat originally weighed 3-1 /3 grains but now it weight 3-1 /5 grains. 150 Carats make the Troy ounce of 480 grains.

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