Question

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.​

Answer 1

Step-by-step explanation:

Let x be the unit digit of the number.

Then, the ten's digit = 11 – x

Therefore, Number = 10(11 - x) +x 110 - 10x +x = 110 – 9x

When digits are interchanged,

unit digit=11 – x and tens digit = x

So, number obtained by interchanging

the digits = 10x + (11 – x) = 9 x +11

As per the question-

9x +11 - (110 – 9x) = 9

⇒ 9x + 11 - 110 + 9x = 9

⇒ 18x + 11 110 = 9

⇒ 18x = 9 - 11+ 110

⇒ 18x = 108

⇒ x= 6

Hence, unit's digit = 6 and tens digit = 11 - 6 = 5.

Therefore, the required number is 56.

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Answer 2

the reqiured no. is 56

Step-by-step explanation:

let x be the unit digit of number.

then, the ten's digit = 11 - x

therefore, number = 10(11-x)+x =

110-10x+x = 110-9x

when digit are interchanged,

unit digit = 11-x and tens digit = x

so, number obtained by interchanging the digit =

10x + (11-x) = 9x + 11

As per the question

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

then do this solution by yourself

x = 6

hence, unit digit = 6 and tens digit = 11-6 = 5

Therefore the required number is ≈ 56