The difference between a 2-digit number obtained by interchanging its digits is 63. What is the difference between the digits of the number? Solve with linear equation with two variable
Answers
1) Let us take the two- digit number as 'XY'
2) As given,
(i) X * Y = 14
(ii) XY + 45 = YX
3) This determines the fact that : XY is a two-digit number with formula "10X + Y"
Similarly, YX is equal to "10Y + X"
4) Therefore, XY + 45 = YX can be rewritten as "10X+Y+45=10Y+X" and hence, X - Y = -5 (eq-1)
5) Secondly, X*Y=14(eq-2)
6) Hence, we can use the formula : (X-Y)^2 = X^2 + Y^2 - 2XY, By replacing the values in eq-1&2, we would get the equation such that:"x^2+Y^2=53"(eq-3)
7) By using the formula : (X+Y)^2 = X^2 + Y^2 + 2XY, we could replace the values in eq-3&2 to get the answer X + Y = 9 (eq-4)
8) In equations 1&4, we could add the L.H.S and R.H.S seperately and equalise them to get answer XY = 27
9) Hence, the required number is 27