Question

. The ratio of tens digit to the unit digit of a two digit number is 2:3. If 27 is added to the number, the digits interchange their places, find the number?

Answer 1

Let the digits of number be x and y, with x being tens digit and y the other.

So, our number is= 10x + y

Now, we are given the ratio

x/y = 2/3

Now, 27 is added to number and number reverses digits,so

10x + y + 27 = 10y + x

9x - 9y = -27....(1)

Now, we know x/y = 2/3

or we can say 3x = 2y

or, 9x = 6y....(2)

Putting this value in (1) we get

6y - 9y = -27

-3y = -27

y = 9

So, x = 2/3 * y = 2/3 * 9 = 6

Our number is 69

Answer 2

Let two digit number is xy = y + 10x , here y is unit digit and x is tens digit.
A/C to question,
Ratio of tens digit to unit digit = 2 : 3
⇒ x/y = 2/3
⇒3x = 2y ------(1)

Now, 27 is added to the number, digits interchange their places.
e.g., y + 10x + 27 = x + 10y
9y - 9x = 27
y - x = 3 ⇒y = x + 3 , put it in equation (1)

3x = 2(x + 3)
⇒3x = 2x + 6
⇒x = 6 and now, y = x + 3 = 6 + 3 = 9

Hence, Number = y + 10x = 9 + 10 × 6 = 69