The Number and the Square

                       In the diagram the numbers from 1to 9 are arranged in a square in such a way that the number in the second row is twice that in the first row and the number in the bottom row three times that in the top row.

                     I am told that there are three other ways of arranging the numbers so as to produce the same result.

 Can you find the other three ways?

1            9                2

3            8                4

5            7                 6

Answer: While the first was the example given, the top row must be one of the four following numbers: 192.219.273 or 327.

The faulty Machine

                 A factory manufacturing flywheels for racing cars has ten machines to make them. The manufacturer knows the correct weight for a flywheel.

                However, one day one of the machines begins to produce faulty parts – either overweight or under- Weight.

               How can the manufacturer find the faulty machine in only two weightings?

Answer: 

                 The manufacturer must take one flywheel made by each machine, find their total weight and compare this with the weight of the equivalent number of good flywheels to obtain the difference.

                 Then, he must take 1 flywheel from machine number one, 2 flywheels from machine number two and so forth and weigh these against the correct weight for that number of parts. 

The Digital Game

                  There is a number, the second digit of which is smaller than its first digit by 4, and if the number was divided by the digits, sum, and the quotient would be 7.

                 Can you find the number?

Answer:  The number is 84.

Something for Profit

             A friend of mine bought a used pressure cooker for Rs. 60. She somehow did not find it useful and so when a friend of hers offered her Rs. 70 she sold it to her. However, she felt bad after selling it and decided to buy it back from her friend by offering her Rs. 80. 

            After having bought it once again she felt that she did not really need the cooker. So she sold it at the auction for Rs. 90.

            How much profit did she make? Did she at all make any profit?

Answer: 

The woman made altogether Rs.20. She made Rs. 10 when she sold the item for the first time and another Rs. 10 when she sold it for the second time.

The Train and the Cyclist

                           A railway track runs parallel to a road until a bend brings the road to a level crossing. A cyclist rides along to work along the road every day at a constant speed of 12 miles per hour.

                         He normally meets a train that travels in the same direction at the crossing.

                        One day he was late by 25 minutes and met the train 6 miles ahead of the level crossing. Can you figure out the speed of the train?

Answer:  

Let’s assume that the man and the train normally meet at the crossing at 8 A.M. then the usual time of the cyclist at the bend is 8 A.M. and he is 6 miles behind at 7.30 A.M. But when the cyclist is late, he arrives at the bend at 8.25 A.M. and therefore he is six miles behind at 7.55 A.M. Since the train takes 5 minutes to travel the six mile run, the speed of the train is 72 m.p.h.

Walking all the Way

              One day I decided to walk all the way from Bangalore to Tumkur. I started exactly at noon. And someone I know in Tumkur decided to walk all the way to Bangalore from Tumkur and she started exactly at 2 p.m. on the same day.

             We met on the Bangalore- Tumkur road at five past four, and we both reached our destination at exactly the same time. At what time did we both arrive?

Answer: 

 

          The key to the solution is that with a little bit of pencil work, it will be found, while I can walk 5 miles, my friend who started from Tumkur can walk 7 miles. Let’s assume the distance between Bangalore and Tumkur is 24 miles, then the point of meeting would be 14 miles from Bangalore , and therefore , I walked 3 ³⁄₇ miles per hour while my friend walked 4 ⁴⁄₅ miles per hour, and we both arrived exactly at 7 P. M.