# Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

**Solution:**

Let the digits at tens place and ones place be x and 9 - x

Therefore, original number = 10x + (9 - x) = 9x + 9

On interchanging the digits, the digits at ones place and tens place will be x and 9 - x respectively.

Therefore, the new number after interchanging the digits = 10(9 - x) + x = 90 - 9x

New number = Original number + 27

90 - 9x = 9x + 9 + 27

90 - 9x = 9x + 36

Transposing 9x to RHS and 36 to LHS, we obtain

90 - 36 = 18x

54 = 18x

Dividing both sides by 18, we obtain

x = 3

Hence, 9 - x = 6

Hence, the digits at tens place and one's place of the number are 3 and 6 respectively. The number is 36.

**Video Solution:**

## Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

NCERT Solutions Class 8 Maths Chapter 2 Exercise 2.4 Question 3

**Summary:**

Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. The two-digit number is 36.

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