. Raj writes a number. He sees that the number of two digits exceeds four times the sum of its digits by 3. If the number is increased by 18, the results is the same as the number formed by reversing the digits. Find the next immediate prime greater than the number.

• ans. 37
  10x+y=4(x+y)+3.......... i
  10x+y+18=10y+x ............. ii
  On solving the above equations we get
  x=3 and y=5
  So. the next immediate prime no. will be 37.
  
• 10 years agoHelpfull: Yes(17) No(2)
• It is a property of numbers like
  difference between a two digit number and digit formed by reversing its digits is always divisible by 9
  i.e.
  if XY is a two digit number and reversed Number is YX
  then YX-XY or XY-YX will be divisible by 9
  and the quotient which will come after dividing will be the difference between digits of a two digit number
  So according to second line
  XY+18=YX
  YX-XY=18
  18/9=2
  so difference between two digit number must be 2
  so number may be
  13or 31,24or42,35or53,46or64,57or75 and so on
  now according to first condition in question
  XY-3(X+Y)=3
  so number 35 satisfies this condition
  Now next prime number after 35 is 37(ANS)
• 10 years agoHelpfull: Yes(4) No(0)
• 10x+y=3+4(x+y)
  9x-9Y=-18
  num=11
  ans)13
  
• 10 years agoHelpfull: Yes(0) No(5)