33. A man can walk uphill at the rate of 2 1/2 kilometers/hour and downhill at the rate of 3 1/4 kilometers per hour. If the total time required to walk a certain distance up the hill and return to the starting point was 4 hours and 36 minutes, what was the distance he walked up the hill?

34. ABC is a right-angled triangle, right-angled at A and AD is the altitude on BC. If AB:AC=3:4, what is the ratio BD:DC?

35. If the roots of the equation

I found these puzzles in the system I am now using. Some user had left them without deleting!

38. A young man has $ 100 in hand. He has to buy 100 balls. One football costs $15, One Cricket ball costs $1 and one table tennis ball costs 25 cents. He spent the entire $ 100 to buy the balls. How many of each balls he bought?   

39. The distance between Station Atena and Station Barcena is 90 miles. A train starts from Atena towards Barcena. A bird starts at the same time from Barcena straight towards the moving train. On reaching the train, it instantaneously turns back and returns to Barcena. The bird makes these journeys from Barcena to the train and back to Barcena continuously till the train reaches Barcena. The bird finally returns to Barcena and rests. Calculate the total distance in miles the bird travels in the following two cases: 
(a) The bird flies at 90 miles per hour and the speed of the train is 60 miles per hour. 
(b) the bird flies at 60 miles per hour and the speed of the train is 90 miles per hour


40. A tennis championship is played on a knock-out basis, i.e., a player is out of the tournament when he loses a match.
(a) How many players participate in the tournament if 15 matches are totally played? 
(b) How many matches are played in the tournament if 50 players totally participate?


41. When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now?   


42. A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked, "How many gold coins do we have?" After pausing a moment, he replied, "Well! If I divide the coins into two unequal numbers, then 37 times the difference between the two numbers equals the difference between the squares of the two numbers."  The wife looked puzzled. Can you help the merchant's wife by finding out how many gold coins he had?


43. A set of football matches is to be organized in a "round-robin" fashion, i.e., every participating team plays a match against every other team once and only once.  If  21 matches are totally played, how many teams participated?


44. Glenn and Jason each have a collection of cricket balls. Glenn said that if Jason would give him 2 of his balls they would have an equal number; but, if Glenn would give Jason 2 of his balls, Jason would have 2 times as many balls as Glenn. How many balls does Jason have?


45. Suppose 8 monkeys take 8 minutes to eat 8 bananas.
(a) How many minutes would it take 3 monkeys to eat 3 bananas?
(b) How many monkeys would it take to eat 48 bananas in 48 minutes     


46. It was vacation time, and so I decided to visit my cousin's home. What a grand time we had! In the mornings, we both would go for a jog. The evenings were spent on the tennis court. Tiring as these activities were, we could manage only one per day, i.e., either we went for a jog or played tennis each day. There were days when we felt lazy and stayed home all day long. Now, there were 12 mornings when we did nothing, 18 evenings when we stayed at home, and a total of 14 days when we jogged or played tennis. For how many days did I stay at my cousin's place?


47. A 31" x 31" square metal plate needs to be fixed by a carpenter on to a wooden board. The carpenter uses nails all along the edges of the square such that there are 32 nails on each side of the square. Each nail is at the same distance from the neighboring nails. How many nails does the carpenter use? 

For 35, let the roots of
x²+x+1=0 be u,v.
Sum of the roots, u+v=-1,
Product of the roots,uv=1.
We know (u+v)²=u²+v²+2uv or u²+v²= (u+v)²-2uv

For the second equation,
u/v+v/u= (u²+v²)/uv
In x²+ax+b=0, sum of the roots=-a,
Therefore, (u²+v²)/uv=-a,
(-1²-2)/1=-a, -1=-a, a=1.

36. Let x be the length of both the trains.
Since the first train takes 8 seconds to cross the man, and distance travelled is x in 8 seconds, speed=x/8.
Similarly, the speed of the second train = x/13.
Combined speed = x/8+x/13=21x/104.
Distance travelled for two trains to cross each other=2x.
Therefore, time taken=distance/speed.
Time=2x/(21x/104) =2x x 104/21x=208/21 seconds.

No, it is 124.

Thanks for the neat pic, Patrick!

28)  I get 44 times at right angles.  I was too lazy, I only counted 22 from 6am to 6pm.
What is the answer for a seven-hour clock and a fourteen hour day??  Do you know Ganesh?  I don't.
The reason I ask is because with a 12 hour clock the 9 and the 3 are at right angles to the 12 at the top, so
the answer is less than 12 x 2 for 12 hours, but a seven hour clock would be weird, or a 5 hour clock too.
Hmmm....  I'll have to ponder this more later...

or u could

Last edited by Kurre (2006-07-28 23:22:00)

3a) 999 + 9^0(9^0)

3c) 999 + 9^0(9^0)(9^0)(9^0)