Enjoyable questions and problems

  At the request of a few younger students I am going to post easier questions/problems. But we will always have a mix of easy and difficult items to meet the needs of different readers. Just do the ones you can, but at least read all postings. Here are the problems for the coming week. Reply any time by writing in the comment field. a)         Q1)  3*(2/3) -  2 *(3/4)  =   ?                b)       Q2)  What are the roots of the equation    x 2 -5x+6 = 0 c)         Q3)  Sin(60 deg) 2 +Cos(60 deg) 2 = ? d)       Q4)   A vertical lamp post casts the sun’s shadow as long as its own height at a particular time, on a horizontal road. How many degrees above the road’s surface is the Sun at that moment? e)       Q5)  A boat travels an hour at 7 kmph up the river and at 5 kmph down the river till it reaches the starting point. How long would the return part of the journey take? The boat's speed is measured relative to the water.

  Gopal runs a shop for which he buys 700 Rs worth of supplies every morning. He pays tax of 20 % on the sale value every evening. He takes the balance home. How much should he sell every day if he has to keep Rs 700 for buying supplies next day and get Rs 300 for his personal expenses of the day? Type in your answer in the comments page. The answer would be moderated and published within 48 hours.  Srinivasan Ramani 

Find a formula   Suppose Biden and Trump stand for election to a golf club which has a hundred members. The one among them who gets more votes would be accepted as a new member. Sometime during the counting, the secretary of the club comes out and says that one person has got 49 votes and the other has got 36 votes as of that moment. The remaining votes are being counted. Someone says, since one has already got 49 votes, why don’t we stop the count and declare him the winner?   The Secretary says, "No. we have to be mathematically sure that one candidate has such a lead that he canot be defeated if the election continues".      Let H be the votes earned by the leading candidate by that time. Let L be the votes earned by the other  candidate by that time. The total number of votes distributed, one per member = 100 Please note all members may not vote. Write the stopping condition in terms of H, L or both.   If the condition is satisfied, we should be able to stop the

About this blog  The content of this blog would be educational, mostly meant for young people in age range of 8 to 16. However, if you find the blog interesting or useful, you are welcome to benefit from it at any age. You can also use the questions and problems published here to test your parents or brothers and sisters!   There is a sister blog https://Stimulate-YourChilds-Mind.blogspot.com designed for youger children - those in the age group of 4-8.   Enjoy! Srinivasan Ramani