When we multiply a two digit number by sum of its digits 144 is achieved. If we reverse the number and multiply it by sum of digits,we get 252. What is the last digit of original number ?

• let the number as 10x+y where x is the digit of unit place and y is other digit.
  Given (10x+y)(x+y)=144
  10x^2+2xy+y^2=144 eq 1
  and (10y+x)(x+y)=252
  10y^2+2xy+x^2=252 eq 2
  eq2 - eq1 = 9y^2-9x^2=108
  => y^2-x^2=12.
  if y=4 & x=2 then number will be 24 which satisfies all given conditions.
  ans. 24.
• 9 years agoHelpfull: Yes(7) No(0)
• Last digit is 4
  24*6=144;
  42*6=252.
  
  
• 9 years agoHelpfull: Yes(2) No(0)
• xy(10x+y)=144
  yx(10y+x)=252
  From this 2 equations we get y=2x.substuting in any one of the eqaution we get x=cube root of (6).by substuting value of x.we get y =2*cuberoot of(6).so we get value as 3.6342=4
• 9 years agoHelpfull: Yes(2) No(6)
• 24*6=144 so original no.is 24 n ans is 4
• 9 years agoHelpfull: Yes(1) No(0)
• answer is 4.
  The original number is 24. Best way to find answer is going through options.
• 9 years agoHelpfull: Yes(1) No(0)
• 24*(2+4)=144 and its reverse 42*(4+2)=251...so ans is 4...by raj gautam
• 9 years agoHelpfull: Yes(1) No(0)
• 24 is the number 24*6=144
  reverse 42*6=252
  last digit of original number is 4
• 9 years agoHelpfull: Yes(0) No(0)
• ans is 4
  because we get the expression y^2-x^2=12 and only x=2 and y=4 is satisfying this equation.
• 9 years agoHelpfull: Yes(0) No(0)
• trick 144 then last digit must be 4 and when we get again 4 when multiplied by 6 so 10th place is 6-4 =2
  
  same for 252 last digit of number is also 2 and when we get last digit 2 in 2s table 6 so first digit is 6-2 =4
• 9 years agoHelpfull: Yes(0) No(0)