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Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.

Solution:

Given, the sum of the digits of a two-digit number is 11.

The given number is less than the number obtained by interchanging the digits by 9.

We have to find the number.

Let the unit’s digit be x

Ten’s digit = 11 - x

Number = 10(11 - x) + x

= 10(11) - 10(x) + x

= 110 - 10x + x

= 110 - 9x

Number obtained by interchanging the digits = 10x + (11 - x)

= 10x - x + 11

= 9x + 11

According to the question,

9x + 11 - (110 - 9x) = 9

9x + 11 - 110 + 9x = 9

18x - 99 = 9

By transposing,

18x = 9 + 99

18x = 108

x = 108/18

x = 54/9

x = 6

Unit’s digit = 6

Ten’s digit = 11 - 6 = 5

Therefore, the required number is 56.

✦ Try This: Sum of the digits of a two-digit number is 33. The given number is less than the number obtained by interchanging the digits by 11. Find the number.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 2

NCERT Exemplar Class 8 Maths Chapter 4 Problem 89

Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.

Summary:

Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. The number is 56

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