self Maths Puzzle

The square of a two digit number is divided by half the number. After 36 is added to the quotient, this sum is then divided by 2. The digits of the resulting number are the same as those in the original number, but they are in reverse order. The ten's place of the original number is equal to twice the difference between its digits. What is the number?

Read Solution (Total 1)

let the digits be x and y. then the number is 10x+y
given: (10x+y)^2/[(10x+y)/2]=2(10x+y).
[2(10x+y)+36]/2=10y+x
or, 10x+y+18=10y+x
or, 9y=9x+18
or, y=x+2
therefore, 10x+y=13,24,35,46,57,68,79
hence there are 7 such two digit numbers
10 years agoHelpfull: Yes(3) No(2)

self Other Question

A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice. Each cat killed more mice than there were cats. How many cats do you think there were ? A wizard named Nepo says "I am only three times my son's age. My father is 40 years more than twice my age. Together the three of us are a mere 1240 years old." How old is Nepo?