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

Required no. = 10y + x

According to the question,

y - 2x = 2

-2x + y = 2                   ...(1)

and,

(10x + y) -3 (y + x) = 5

7x - 2y = 5                   ...(2)

Multiplying equation no. (1) by 2.

 - 4x + 2y = 4              ...(3)

Now adding (2) and (3),
       -4x + 2y = 4
+      7x - 2y = 5  
           3x = 9
            x = 3

From (1), we get

-2(3) + y = 2

y = 8

Required number is 10(8) + 3 = 83