In a number of two digits the ratio of digit in tens place and the digit in unit place is 3 is to 1 if 3 is added to the three times the sum of the digit and the opposite number is formed find the numbers

The number is 93 .

Step-by-step explanation:

Given as :

Let The two digit number = 10 x + y

The ratio of tens digit to unit digit = 3 :1

I.e =  

Or, x = 3 y           ...1

Again

If 3 is added to the three times the sum of the digit and the opposite number is formed

The opposite number will be 10 y + x

So, 3 × (x + y) + 3 = 10 y + x

Or, 3 x + 3 y + 3 = 10 y + x

Or, 3 x + 3 y + 3 - 10 y - x = 0

Or, 2 x - 7 y + 3 = 0

Or, 7 y - 2 x = 3             ........2

Now, Solving eq 1 and 2

7 y - 2 × 3 y = 3    

Or, 7 y - 6 y = 3

Or, y = 3

Now, put the value of y into eq 1

∵ x = 3 y

So, x = 3 × 3

i.e x = 9

So, The number = 10 x + y

i.e The number = 10 × 9 + 3

Or,  The number = 93

Hence, The number is 93 . Answer