Question

Q9. 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

Answer:

Given :-

• 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.

To Find :-

• What is the number.

Solution :-

Let,

➢ Unit's digits = x

➢ Ten's digit = 11 - x

Then, the number will be :

➳ Number = 10(11 - x) + x

➳ Number = 110 - 10x + x

➳ Number = 110 - 9x

➼ Number = 110 - 9x

Now,

$\leadsto$ The number obtained by interchanging we get,

➧ 10x + (11 - x)

➧ 10x + 11 - x

➧ 10x - x + 11

➪ 9x + 11

According to the question,

➵ 9x + 11 - (110 - 9x) = 9

➵ 9x + 11 - 110 + 9x = 9

➵ 9x + 9x = 9 - 11 + 110

➵ 18x = 108

➵ x = 108/18

➵ x = 6/1

➽ x = 6

Hence, the required original number is :

➸ Original Number = 110 - 9x

➸ Original Number = 110 - 9(6)

➸ Original Number = 110 - 9 × 6

➸ Original Number = 110 - 54

➲ Original Number = 56

$\therefore$ The number is 56.

Answer 2

Step-by-step explanation:

given :

• Q9. 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.

to find :

• number obtained by interchanging the digits by 9. Find the number.

solution :

• 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) = 9x + 11

• As per the question

• 9x + 11 (110- 9x) = 9

• ⇒ 9x + 11 - 110 + 9x = 9

• ⇒18x + 11-110 =9

• ⇒18x9-11 + 110

• ⇒18x =108

• ⇒x=6

• Hence, unit's digit = 6 and ten's digit = = 11

• 6 = 5.

• Therefore, the required number is 56.