Question

the sum of the digits of a two-digit number is 5 on adding 27 to the number its digits are reversed find the original number​

Answer 1

Step-by-step explanation:

14

= 1+4=5

= 14+27 = 41 it is reversed to 14

Answer is 14

Answer 2

Answer:

The Original Number is 14.

Step-by-step explanation:

Given :

Sum of the digits = 5

On adding 27 the digits = get reversed

To find :

The Original Number

Solution :

Let the Digits of Original Number be -

• Tens Place as 10(x)
• Units Place as (5 - x)

$\longrightarrow$ 10(x) + (5 - x)

$\longrightarrow$ 10x + (5 - x)

$\longrightarrow$ 9x + 5

$\rule{300}{1.5}$

Number with Reversed Digits -

• Tens Place = 10(5 - x)
• Units Place = (x)

$\longrightarrow$ 10(5 - x) + x

$\longrightarrow$ 50 + 10x - x

$\longrightarrow$ 50 - 9x ...... [Number with Reversed Digits]

$\rule{300}{1.5}$

According to the Question -

After adding 27 to the original number, the number of the digits get reversed.

★ $\boxed{\sf{(50-9x)+27=9x+5}}$

$\sf{\longrightarrow} \: (50-9x)+27=9x+5 \\ \\ \sf{\longrightarrow} \:23 - 9x = 9x + 5 \\ \\ \sf{\longrightarrow} \:23 - 5 = 9x + 9x \\ \\ \sf{\longrightarrow} \:18 = 18x \\ \\ \sf{\longrightarrow} \:x = \dfrac{18}{18} \\ \\ \sf{\longrightarrow} \:x = 1$

$\rule{300}{1.5}$

Original Number =

$\sf{\longrightarrow} \:9x + 5 \\ \sf{\longrightarrow} \:9(1) + 5 \\ \sf{\longrightarrow} \:14$

$\therefore$ The Original Number is 14.