Question

i) The sum of the digits of a two-digit number is 9. Also, nine times this number is
twice the number obtained by reversing the order of the digits. Find the number.​

Answer 1

EXPLANATION.

Let the ten's place be = x

Let the unit place be = y

original number = 10y + x

reversing number = 10x + y

To find the number.

According to the question,

Case = 1.

sum of the digit of two digit number = 9

=> x + y = 9 .......(1)

Case = 2.

Nine times this number is twice the number

obtained by reversing the order of digit.

=> 9 ( 10y + x) = 2 ( 10x + y)

=> 90y + 9x = 20x + 2y

=> 88y = 11x

= 8y = x .....(2)

put the value of x = 8y in equation (1)

we get,

=> 8y + y = 9

=> 9y = 9

=> y = 1

put the Value of y = 1 in equation (2)

we get,

=> x = 8(1)

=> x = 8

Therefore,

original number = 10y + x

=> 10 X 1 + 8

=> 18

original number = 18

Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• The sum of the digits of a two-digit number is 9.

• Nine times this number is twice the number obtained by reversing the order of the digits.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The original number.

$\bf{\underline{\underline\green{Solution:-}}}$

Let the tens digit of the number be x

The ones digit of the number be y

The original number = 10x + y

The reversed number = 10y + x

According to the 1st condition:-

The sum of digits of the number is 9

So:-

→ x + y = 9.........(i)

According to the 2nd condition:-

Nine times this number is twice the number obtained by reversing the order of the digits.

→ 9 × original number = 2 × reversed number

→ 9( 10x + y ) = 2(10y + x)

→ 90x + 9y = 20y + 2x

→ 90x - 2x + 9y - 20y = 0

→ 88x - 11y = 0

Dividing the equation by 11

→ 8x - y = 0........(ii)

Adding equation (i) and (ii)

→ (x + y) + ( 8x - y ) = 9 + 0

→ x + y + 8x - y = 9

→ 9x = 9

→ x = 1

Substituting x = 1 in equation (i)

→ x + y = 9

→ 1 + y = 9

→ y = 9 - 1

→ y = 8

The original number

= 10x + y

= 10( 1) + 8

= 10 + 8

= 18

Therefore, The original number = 18