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:
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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