Question

Ratio of ten digit to ones digit of a 2 digit number is 2:3. If 27 is added to the number, the digits interchange their places. Find the number.​

Answer 1

Answer:

69

(69+27=96)

Step-by-step explanation:

see the attachment for explanation.

Answer 2

Answer:

The two digit number is 69 .

Step-by-step explanation:

Given as :

Ratio of ten digit to ones digit of a 2 digit number is 2:3

Let The two digit number = 10 x + y

According to question

$\dfrac{x}{y}$ = $\dfrac{2}{3}$

Or, 3 x = 2 y

Or, 3 x - 2 y = 0                 .......A

Again

If 27 is added to the number then digits are interchanged

So, (10 x + y) + 27 = 10 y + x

Or, (10 y - y ) + (10 x - x ) = 27

Or, 9 y - 9 x = 27

Or, y - x = $\dfrac{27}{9}$

i.e y - x = 3                        ...........B

Now, Solving eq A and eq B

(3 x - 2 y) + 2 × (y - x) = 0 + 2 × 3

Or, (3 x - 2 x) + ( - 2 y + 2 y) = 6

Or, x + 0 = 6

i.e x = 6

So, The value of x = 6

Now, Put the value of x into eq B

∵  y - x = 3

Or, y - 6 = 3

or, y = 3 + 6

i.e y = 9

So, The value of y = 9

∵, The two digit number = 10 x + y

i.e  The two digit number = 10 × 6 + 9

Or, The two digit number = 60 + 9

∴ The two digit number = 69

Hence, The two digit number is 69 . Answer