Question

A two-digit number is such that the ten’s digit exceeds twice the unit’s digit by 2 and the number obtained by inter-changing the digits is 5 more than three times the sum of the digits. Find the two digit number.

Answer 1

Let the digit in a unit’s place be x and the digit at ten’s place be y.

Required number = 10y + x,

According to the given conditions,

y − 2x = 2

−2x + y = 2   ...(1)

And,

(10x + y) − 3 (y + x) = 5

7x − 2y = 5   ...(2)

Multiplying equation (1) by 2,

2(−2x + y) = 2(2)

−4x + 2y = 4   ...(3)

Now adding equations (2) and (3),

    −4x + 2y = 4
+    7x − 2y = 5 
               3x = 9
              ∴ x = 3

Substituting x = 3 into equation (1), we get,

−2(3) + y = 2

−6 + y = 2

y = 2 + 6

∴ y = 8

Here, required number = 10y + x,

= 10(8) + 3

= 80 + 3

= 83

Hence, the required number is 83.