Question

In a two digit number, the unit’s digit is twice the ten’s digit . If 27 is added to the number. the digits interchange their paces. Find the number.

Answer 1

Answer:

The number is 36.

Step-by-step explanation:

Let the tens digit no. be x, then unit digit no will be 2x

now value from x and 2x will be:

10*X+2x = 12x.

now, when 27 will be added si digits will interchange their places

then unit digit = x

and tens digit= 2x

then value obtained from these digits will be :

10*2x + x = 21x

now according to question:

12x +27= 21x

12x-21x= -27

-9x=-27

x = -27/-9

x= 3

now the real value is 12x

so on placing value of x

we get:

12×3

=36

so 36 is the required number.

HOPE IT WILL BE HELPFUL !!

Answer 2

Answer:

⍟ Let the digits be x and y

Now,

according to the given question :

$</em></strong><strong><em>2</em></strong><strong><em>x = y......(1)$

Let the original number be 10x + y

Given that :

$10x + y + 27 = 10y + x......(2)$

Now , after substituting the values of equation (1) in equation(2) ,we get :

$10</em></strong><strong><em>x</em></strong><strong><em> + </em></strong><strong><em>2</em></strong><strong><em>x</em></strong><strong><em> </em></strong><strong><em>+ 27 = 10y + </em></strong><strong><em>x</em></strong><strong><em>$

$\implies \: </em></strong><strong><em>1</em></strong><strong><em>2</em></strong><strong><em>x</em></strong><strong><em> </em></strong><strong><em>+ 27 = </em></strong><strong><em>2</em></strong><strong><em>0</em></strong><strong><em>x</em></strong><strong><em>+</em></strong><strong><em>x</em></strong><strong><em>$

$\implies \: </em></strong><strong><em>1</em></strong><strong><em>2</em></strong><strong><em>x</em></strong><strong><em>+ 27 = </em></strong><strong><em>2</em></strong><strong><em>1</em></strong><strong><em>x</em></strong><strong><em>$

$\implies \: </em></strong><strong><em>2</em></strong><strong><em>7</em></strong><strong><em> = </em></strong><strong><em>2</em></strong><strong><em>1</em></strong><strong><em>x</em></strong><strong><em>-</em></strong><strong><em>1</em></strong><strong><em>2</em></strong><strong><em>x</em></strong><strong><em>$

$\implies \:</em></strong><strong><em> </em></strong><strong><em>9</em></strong><strong><em>x</em></strong><strong><em>=</em></strong><strong><em>2</em></strong><strong><em>7</em></strong><strong><em> </em></strong><strong><em>$

$\implies \: </em></strong><strong><em>x</em></strong><strong><em> = \frac{ </em></strong><strong><em>2</em></strong><strong><em>7</em></strong><strong><em>}{9}$

$\implies \: = 3$

Its given that unit digit is twice the tens digit .

Now , x = 3

so ,the unit digit will be twice the tens digit = 3×2 = 6

➪ Therefore ,the given number is $\bf{\orange{\underline{36}}}$