sum of the digit of a two digit number is 9 when we interchange the digits it is found that the resulting number is greater than the original number by 27 what is the two digit number ?
Answers
Answer:
The new number is greater than the old number by 27, i.e. Adding the two equations, we get 2y = 12 or y = 6. Thus, x = 3. Therefore, the original number is 36.
Given data : Sum of the digit of a two digit number is 9 when we interchange the digits it is found that the resulting number is greater than the original number by 27.
To find : What is the two digit number ?
Solution : Sum of the two digit number is 9.
Let, unit/one's place digit be x
Hence, unit/one's place digit is 9 - x
- Units/one's place digit, x = x ----{1}
- Ten's place digit, y = 9 - x ----{2}
So, here,
Number is represented by 10y + x
Hence,
➜ Original number = 10y + x
➜ Original number = 10 * (9 - x) + x ----{3}
➜ Original number = 90 - 10x + x
➜ Original number = 90 - 9x
Now, after interchanging the digits;
➜ New number = 10x + y
➜ New number = 10x + (9 - x) ----{4}
➜ New number = 10x + 9 - x
➜ New number = 9x + 9
The resulting number is greater than the original number by 27.
➜ New number = Original number + 27
➜ New number - Original number = 27
➜ (9x + 9) - (90 - 9x) = 27
➜ 9x + 9 - 90 + 9x = 27
➜ 9x + 9x + 9 - 90= 27
➜ 18x - 81 = 27
➜ 18x = 27 + 81
➜ 18x = 108
➜ x = 108/18
➜ x = 6
{Hence, unit/one's place digit is 6}
Put value of x in eq. {3}
➜ Original number = 10 * (9 - x) + x
➜ Original number = 10 * (9 - 6 ) + 6
➜ Original number = 10 * 3 + 6
➜ Original number = 30 + 6
➜ Original number = 36
Answer : Hence, the two digit number is 36.