Question

The sum of the digits of a two digit number is 7. The sum of the number and the number

formed by reversing the digits is 77.Write the linear equations in two variables for the above

statements.​

Answer 1

Let the original number be

yx ; i.e., 10y+x. We know x+y=7. The number obtained by reversing the digits in

xy , i.e., 10x+y. The second condition gives 10x+y−2=2(10y+x). Thus we have two equations:

x+y=7....(1)

8x−19y=2....(2)

Multiply the equation (1) by 19 and get

19x+19y=133.

Adding this to (2), we obtain 27x=135. This gives x=5. Hence y=7−x=7−5=2.

The required number is 25.