Question

5. A number has two digits whose sum is 6. If 36 is added to the number,
its digits gets interchanged. Find the number.

Answer 1

Answer:

Let the number be of the form ‘xy’.

Given, sum of the numbers is 6. So, we write as [x + y = 6] — (1).

Also given, if 36 is added to the number, the digits get reversed.

So, we can write the number as ‘10x+y’.

So, 10x+y + 36 = 10y+x.

We get [y - x = 4] — (2).

From (1) and (2), we get x = 1 and y = 5.

Therefore, the number is ‘15’ .

Step-by-step explanation:

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Answer 2

SOLUTION :-

Let,

Digit in ten's place = x

Digit in one's place - y

Two digit number = 10x + y

According to the first condition,

$\longrightarrow\sf x+y = 6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(1)$

According to the second condition,

$\longrightarrow\sf 10x+y+36= 10y-x \\\\\longrightarrow 10x-x+y-10y = -36 \\\\\longrightarrow 9x-9y = -36 \\\\\longrightarrow x-y = -4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .....................(2)$

Eq (2) + Eq (1),

$\longrightarrow\sf 2x = 2 \\\\\longrightarrow\bf x = 1$

Substitute the value of x in eq (1),

$\longrightarrow\sf 1+y= 6 \\\\\longrightarrow\bf y = 5$

Two digit number = 15