Question

Sum of the digits of a 2-digit number is 8. When we interchange the digits, it is found that the
resulting new number is greater than the original number by 18. Find the number.

Answer 1

ANSWER:

• Original number = 35

GIVEN:

• Sum of the digits of a 2-digit number is 8.
• Interchange the digits, it is found that the resulting new number is greater than the original number by 18.

TO FIND:

• Original number.

SOLUTION:

Let the digit at tens place be 'x'.

Let the digit at once place be 'y'.

Original number= 10x+y

Reversed number = 10y+x

Case 1

=>x+y=8. ......(i)

Case 2

=> 10y+x = (10x+y)+18

=> 10y+x = 10x+y+18

=> 10y-y+x-10x = 18

=> 9y-9x= 18

=> 9(y-x) = 18

=> y-x = 18/9

=> y-x = 2. ......(ii)

Adding eq (i) and (ii) we get;

=> x+y+y-x = 8+2

=> 2y = 10

=> y = 5

Putting y = 5 in eq (i)

=> x+5= 8

=> x = 8-5

=> x = 3

Original number = 10x+y

= 10(3)+5

= 30+5

= 35

Reversed number = 10y+x

= 10(5)+3

= 50+3

= 53