a biker notices a certain number(2 digits number) on the milestone before starting the journey. After riding for an hour he notices a milestone with reversed digits of the previous number. Now after riding for another hour he notices that the number on a new milestone had same digits as the first one (in the same order) but with a "0" between the 2 digits. If the rider maintains a constant speed throughout, Calculate his speed.

• ANS : 45
  
  let first two digit number is xy = 10x + y
  after one hour, the number is reversed yx = 10y + x
  after another one hour, it x0y = 100x + y.
  
  now xy < yx < x0y
  
  so, (10y + x) - (10x + y) = (100x + y) - (10y + x)
  or, 9(y - x) = 9(11x - y)
  or, 12x = 2y
  
  the above equation will be true only if x = 1 and y = 6.
  
  hence, his speed is 45
• 8 years agoHelpfull: Yes(37) No(4)
• let the speed be s kmph,and digits x,y
  then milestones will be 10x+y,10y+x,100x+y
  9y-9x=s;
  99y-9y=s;
  solving we get s=45x;
  y=6x;
  since y is a digit x=1;
  hence y=6;
  s=45 kmph
• 8 years agoHelpfull: Yes(20) No(3)
• ANS : 45
  
  first suppose 12
  then 21
  then 102
  
  difference between 21-12= 9
  then difference between 102-21=81
  
  after that add 81+9 = 90
  because of total houre 2 so that 90/2= 45
  u can choose any number and get the deference then add and
  devide by total hour then find speed
  
• 7 years agoHelpfull: Yes(9) No(0)
• first milestone 16
  second milestone 61
  third milestone 106
  speed 45
  
• 8 years agoHelpfull: Yes(5) No(2)
• let
  first no. is XY then
  second will YX and
  last will X0Y
  
  now assume S is speed then we can say that
  XY+S=YX (1)
  YX+S=X0Y (2)
  put 1 in 2 we get
  2S=X0Y-XY
  now put X and Y any value except 0,0 because speed can't be 0
  s=45
  
  
  so answer is 45
• 8 years agoHelpfull: Yes(5) No(2)
• (10y + x) - (10x + y) = (100x + y) - (10y + x)
  how this equation comes
  
  
• 8 years agoHelpfull: Yes(4) No(2)
• YX-XY=X0Y-YX;
  X can be only 1 or 2 as deviations from other numbers are huge.
  when we plug in the value of x=1 and y=6 in the equation above, we get LHS=RHS=45. which is the constant speed at which he is travelling ie., 45KM/hr
• 8 years agoHelpfull: Yes(1) No(0)
• why x=1 and y=6..??
• 8 years agoHelpfull: Yes(1) No(0)
• According to me, the speed should be 45. correct me if I am wrong
  
• 8 years agoHelpfull: Yes(0) No(0)
• 45 is correct
• 8 years agoHelpfull: Yes(0) No(0)
• XY-YX=YX-X0Y;
  X can be only 1 or 2 as deviations from other numbers are huge.
  when we plug in the value of x=1 and y=6 in the equation above, we get LHS=RHS=45. which is the constant speed at which he is travelling ie., 45KM/hr
• 8 years agoHelpfull: Yes(0) No(0)