Question

The sum of the digits of a 2 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 :

The number is 56

Explanation :

Let,

• One digit be x
• Tens digit be y.

=> The number is xy

Given,

• Sum of x and y is 11

$\implies \: x + y = 11$

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

=> Let, the interchanged number be yx.

$\implies \: 10x + y = 10y + x - \: 9$

$\implies \: 10x - x - 10y - y = ( - 9)$

$\implies \: 9x - 9y = ( - 9)$

$\implies \: x - y = ( - 1)$

We got, two Equatios ,

x + y = 11 and x - y = (-1)

• Add both the equations.

$\implies \: 2x - y + y = 11 - 1$

$\implies \: 2x = 10$

$\implies \: x = \frac{10}{2}$

$\implies \: x \: = 5$

Therefore, the Value of x is 2.

• Replace the value of x in any equation.

$\implies \: 5 - y = ( - 1)$

$\implies \: - y = (-1-5)$

$\implies \: y = 6$

Therefore, the value of y is 6

Number : XY = 56

Therefore, the number to be found is 56.

Answer 2

ANSWER :–

56

EXPLANATION :–

=> LET THE IS "XY".

• ACCORDING TO THE QUESTION ,

SUM OF DIGITS IS 11 .

SO , THAT —

=> X + Y = 11 .........(1)

• ACCORDING TO THE QUESTION ,

THE GIVEN NUMBER IS LESS THEN

THE NUMBER OBTAINED BY INTER

CHANGING THE DIGIT BY 9.

SO , THAT –

=> 10 X + Y = (10 Y + X) - 9

=> 10 X + Y = 10 Y + X - 9

=> 9 X = 9 Y - 9

=> X - Y = - 1 ........(2)

● NOW ADD EQUATION (1) AND (2) —

=> 2 X = 10

=> X = 5

● PUT THE VALUE OF 'X' IN EQUATION

(1) —

=> 5 + Y = 11

=> Y = 6

☆☆☆ HENCE , THE NUMBER IS 56 . ☆☆☆