Question

(3)
A number consists of two digits whose sum is 6. If 8 is added to the number, the digits are reversed.
find the number​

Answer 1

Correct Question:

A number consists of two digits whose sum is 6. If 18 is added to the number, the digits are reversed. Find the number

Answer:

The Original Number is 24.

Step-by-step explanation:

Given :

Sum of the digits = 6

When 18 is added = the digits of the number get reversed.

To find :

The Original Number

Solution :

$\textsf{\underline{\underline{Original number : }}}$

$\textbf{\small{\underline{Let the digits be -}}}$

• Units Place be as y
• Tens Place be as 10(6 - y)

⇒ 10(6 - y) + y

⇒ 60 - 10y + y

⇒ 60 - 9y ......... [Original Number]

$\rule{300}{1.5}$

$\textsf{\underline{\underline{Number with Reversed Digits :}}}$

$\textbf{\small{\underline{Let the digits be - }}}$

• Units Place as (6 - y)
• Tens Place as 10(y)

⇒ 10(y) + (6 - y)

⇒ 10y + 6 - y

⇒ 9y + 6 ......... [Number with Reversed Digits]

$\rule{300}{1.5}$

$\textsf{\underline{\underline{According to the Question : }}}$

If 8 is added to the number, the digits are reversed.

⇒ (60 - 9y) + 18 = 9y + 6

⇒ 78 - 9y = 9y + 6

⇒ 78 - 6 = 9y + 9y

⇒ 72 = 18y

⇒ y = 72/18

⇒ y = 4

$\rule{300}{1.5}$

★ Value of 60 - 9y

⇒ 60 - 9(4)

⇒ 60 - 36

⇒ 24

Original number = 24

$\therefore$ The Original Number is 24.

Answer 2

Answer:

The required number is 24.

Step-by-step explanation:

The Accurate Question :

A number consists of two digits whose sum is 6. If 18 is added to the number, the digits are reversed.  Find the number​.

Solution :

Consider the :

The digit at tens place as - x.

Now, As given,

The sum of two digits is 6.

So,

If the digit at tens place is x.

Then,

The digit at ones place = 6 - x

So, The number formed will be $\sf 10x + 6-x = 9x+6$

Also given,

The digits are reversed.

So,

$\sf \implies 10(6-x) + x= 60-10x+x = 60-9x$

According to the question,

$\sf \\ \\\implies 9x+6 + 18 = 60-9x\\ \\ \\ \implies 9x+24 = 60-9x\\ \\ \\ \implies 9x+9x = 60-24\\ \\ \\ \implies 18x = 36\\ \\ \\ \implies x = \dfrac{36}{18}\\ \\ \\ \implies x = 2\\ \\ \\ \implies 9x+6 = 9(2)+6 = 18+6 = 24$

∴ The required number is 24.