Question

Sum of digits of a two-digit no. Is 9. When the digits are interchanged and 18 is substracted from the new no. The resulting no. Is greater than the original no. By 9 . What is the two digit no.?

Answer 1

Answer:

The Original Number is 36.

Step-by-step explanation:

Given :

Sum of the digits of the Number = 9

Number with revered digits is when subtracted by 18 = resulting number is greater tham original by 9

To find :

The number

Solution :

$\textbf{\small{\underline{The Original Number =}}}$

Let the -

• Units Place be x
• Tens Place be 10(9 - x)

Original number = 10(9 - x) + x

$\longrightarrow$ 90 - 10x + x

$\longrightarrow$ 90 - 9x .......[Original Number]

$\rule{300}{1.5}$

$\textbf{\small{\underline{Number with Reversed Digits =}}}$

Let the -

• Units place be (9 - x)
• Tens place be 10(x)

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

$\longrightarrow$ 10x + 9 - x

$\longrightarrow$ 9x + 9 ........[Number with Reversed Digits]

$\rule{300}{1.5}$

$\textbf{\small{\underline{According to the Question -}}}$

Number with revered digits is when subtracted by 18 = resulting number is greater tham original by 9

$\sf{\longrightarrow} \: (9x + 9) - 18 = (90 - 9x) + 9 \\ \sf{\longrightarrow} \: 9x - 9 = 99 - 9x \\ \sf{\longrightarrow} \: 9x + 9x = 99 + 9 \\ \sf{\longrightarrow} \: 18x = 108 \\ \sf{\longrightarrow} \: x = \frac{108}{18} \\ \sf{\longrightarrow} \: x = 6$

$\rule{300}{1.5}$

$\textbf{\small{\underline{Original Number =}}}$

$\sf{\longrightarrow} \: 90 - 9x \\ \sf{\longrightarrow} \: 90 - 9(6) \\ \sf{\longrightarrow} \: 90 - 54 \\ \sf{\longrightarrow} \: 36$

$\therefore$ The Original Number is 36.

Answer 2

Answer:

Step-by-step explanation:

Given :-

Sum of digits of a two-digit no. is 9.

When the digits are interchanged and 18 is substracted from the new no.

The resulting no. Is greater than the original no. By 9 .

To Find :-

The two digit no.

Solution :-

Let the digits at tens place and ones place be x and 9 − x .

Original number = 10x + (9 − x) = 9x + 9

On interchanging the digits, the digits at ones place and tens place will be x and 9 − x .

Therefore, new number after interchanging the digits = 10(9 - x) + x

According to the Question

= 90 - 10x + x

= 90 - 9x 90 - 9x

= 9x + 9 + 27 90 - 9

= 9x + 36

Transposing 9x to R.H.S and 36 to L.H.S, we obtain

90 - 36 = 18x

54 = 18x

Dividing both sides by 18, we obtain

3 = x and 9 - x = 6

Therefore, the digits at tens place and ones place of the number are 3 and 6 respectively.

Hence, the two-digit number is 9x + 9 = 9 × 3 + 9 = 36