Question

A two digt number is 7 times the sum of its digit. when 27 is subtracted from the number the digit s are interchanged . find the number​

Answer 1

Answer:

63

Step-by-step explanation:

Let the digit at ones place be x, and

The digit at tens place be y.

Therefore, the number will be (10y+x)

Now, It's Given that,

The number is 7 times the sum of it's digits.

Therey, we will get,

=> 10y + x = 7(x+y)

=> 10y + x = 7x + 7y

=> 6x - 3y = 0

=> y = 2x .......(1)

Now, on interchanging the digits,

New number = (10x+y)

But, It's said that,

It will be equal to 27 less than original number.

Therefore, we will get,

=> 10y + x - 27 = 10x + y

=> 9y - 9x - 27 = 0

=> y - x - 3 = 0

Substituting the value, we get,

=> 2x - x - 3 = 0

=> x -3 = 0

=> x = 3

Therefore, we have,

=> y = 2(3)

=> y = 6

Therefore, we have,

=> 10y + x = 10(6) +3 = 60+3 = 63

Hence, required number is 63.