Question

In a two digit number, the ratio of the digits at the units place and tens place is 3:2. If the digits are reversed, the resulting number is 27 more than the original. Assuming the digit at the units place to be x, obtain an equation. Also find the number.

Answer 1

Digit at unit place is x, let digit at tens place is y, then-
x:y = 3:2
or $\frac{x}{y} = \frac{3}{2}$ -> 2 * x = 3 * y ......eq(1)

The original number is (10 * y + x)
If we reverse the digits get reversed so new number is (10 * x + y)

Now according to the question, (10 * x + y) = (10 * y + x) + 27
-> 9 * x - 9 * y = 27
-> 9 * (x - y) = 27
-> x - y = 3
-> y = x - 3 .......eq(2)

Now substitute value of y from eq(2) to eq(1)
-> 2 * x = 3 * (x - 3)
-> 2 * x = 3 * x - 9
-> x = 9

and y = x - 3 -> y = 6

So the number = (10 * y + x) -> 69

Answer
69

Answer 2

units place=x
tens place= 2/3 x
number value= 10* 2/3 x + x
                   =23/3 x
reverse number value= 10x + 2/3x
                              = 32/3 x
32/3x -23/3x =27
3x=27          x=9
 The number is 69