1. If you look at a clock and the time is 3:15, what is the angle between the hour and the minute hands?
Ans:The answer is 7.5 degrees and not zero. Since, in one minute hour and travels 1 degree so after 15 minutes hour hand will be 7.5 degrees away from 3 where the minute hand is present.
2. There are 2 candles of equal size each of which can burn 1 hour. We have to measure 90 minutes using these candles. There is no scale or clock but a lighter is present ?
Ans: First of all light up both the ends of the 1st candle. When it burns out completely it means 30 minutes has passed. Now,light one end of the 2nd candle. When it burns completely, it means an hour (60 minutes) has passed. Thus, we can measure 90 minutes , that is, 30 + 60 = 90 minutes.
3. Solve the above problem to measure 45 minutes ?
Ans: First of all light up both the ends of the 1st candle and simultaneously light the one end of the 2nd candle.When the 1st candle burns out completely, then light up the both the ends of the 2nd candle.Thus, in first phase we measured 30 minutes and in second phase we measured 15 minutes as the 2nd candle was half its size at the start of second phase which gives us 15 + 30 = 45 minutes.
4. How it is possible to place 4 points that are equidistant from each other?
Or,
Consider yourself as a landscape designer and your boss asked you to design a landscape such that you should place 4 trees at equal distance from each other ?
Ans: In a 2D plane, only 3 points can be equidistant from each other in form of an equilateral triangle . But in a 3D plane, one can place 4 points at equal distance in the form of a tetrahedron.
5. How do you cut a rectangular cake into two equal pieces when someone has already taken a rectangular piece from it? The removed piece can be any size or at any place in the cake. You are only allowed one straight cut.
Ans: Slice the cake horizontally from half the height of the cake.
Ans:The answer is 7.5 degrees and not zero. Since, in one minute hour and travels 1 degree so after 15 minutes hour hand will be 7.5 degrees away from 3 where the minute hand is present.
2. There are 2 candles of equal size each of which can burn 1 hour. We have to measure 90 minutes using these candles. There is no scale or clock but a lighter is present ?
Ans: First of all light up both the ends of the 1st candle. When it burns out completely it means 30 minutes has passed. Now,light one end of the 2nd candle. When it burns completely, it means an hour (60 minutes) has passed. Thus, we can measure 90 minutes , that is, 30 + 60 = 90 minutes.
3. Solve the above problem to measure 45 minutes ?
Ans: First of all light up both the ends of the 1st candle and simultaneously light the one end of the 2nd candle.When the 1st candle burns out completely, then light up the both the ends of the 2nd candle.Thus, in first phase we measured 30 minutes and in second phase we measured 15 minutes as the 2nd candle was half its size at the start of second phase which gives us 15 + 30 = 45 minutes.
4. How it is possible to place 4 points that are equidistant from each other?
Or,
Consider yourself as a landscape designer and your boss asked you to design a landscape such that you should place 4 trees at equal distance from each other ?
Ans: In a 2D plane, only 3 points can be equidistant from each other in form of an equilateral triangle . But in a 3D plane, one can place 4 points at equal distance in the form of a tetrahedron.
5. How do you cut a rectangular cake into two equal pieces when someone has already taken a rectangular piece from it? The removed piece can be any size or at any place in the cake. You are only allowed one straight cut.
Ans: Slice the cake horizontally from half the height of the cake.
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