Question

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

Answer 1

GIVEN:

• The sum of digits of a two digit number is 9.
• Nine times the number is twice the
• number obtained by reversing the order of digits.

TO FIND:

• What is the number ?

SOLUTION:

Let the digit at ten's place be 'x' and the digit at unit's place be 'y'

CASE:- 1)

✍ The sum of digits of a two digit number is 9.

According to question:-

➠ x + y = 9

➠ x = 9 –y....❶

CASE:- 2)

✍ Nine times the number is twice the

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

Reversed Number = 10y + x

9(Original Number) = 2(Reversed Number)

According to question:-

➠ 9(10x + y) = 2(10y + x)

➠ 90x + 9y = 20y + 2x

➠ 90x –2x = 20y –9y

➠ 88x = 11y

Put the value of 'x' from Equation 1) in equation 2)

➠ 88(9 –y) = 11y

➠ 792 –88y = 11y

➠ 792 = 11y + 88y

➠ 792 = 99y

➠ $\sf{\cancel\dfrac{792}{99}}$ = y

❮ 8 = y ❯

Put the value of 'y' in equation 1)

➠ x = 9 –8

❮ x = 1 ❯

◉ NUMBER = 10x + y

◉ NUMBER = 10(1) + 8

◉ NUMBER = 10 + 8

◉ NUMBER = 18

❝ Hence, the number obtained is 18 ❞

______________________

Answer 2

$\huge\underline{\overline{\mathfrak{\color{green}{Given}}}}$

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

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

$\huge\underline{\overline{\mathfrak{\color{green}{To \: Find}}}}$

• The number

$\huge\underline{\overline{\mathfrak{\color{green}{Solution}}}}$

Let, the tens place digit number be x and the unit's place digit be y.

According to the first condition,

$\rm{x + y = 9}$

$\rm{\implies x = 9 - y }$--------(1)

$\rule{300}{2}$

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

Original number= 10x + y

Reversed Number = 10y + x

According to the second condition,

$\rm{9(10x + y) = 2(10y + x)}$

$\rm{\implies 90x + 9y = 20y + 2x}$

$\rm{\implies 90x - 2x = 20y - 9y }$

$\rm{\implies 88x = 11y}$

Now by putting the value of x from eq(1)

$\rm{\implies 88(9 - y) = 11y}$

$\rm{\implies 792 - 88y = 11y}$

$\rm{\implies 792 = 11y + 88y}$

$\rm{\implies 792 = 99y}$

$\rm{\implies \cancel \frac{792}{99} = y}$

$\rm{\implies y = 8}$

Now by putting the value of y in eq(1)

$\rm{x = 9 - y}$

$\rm{\implies x = 9 - 8}$

$\rm{\implies x = 1 }$

Number = 10x + y

Number= 10(1) + 8

Number = 10 + 8

Number= 18

Hence, the number is 18.

$\rule{300}{2}$