Question

Sum of the digit of a two digit no. is 5. when digits are interchanged, the resulting no. is greater than original no. by 27. find that no. .​

Answer 1

Answer:

The original number is 14

Step-by-step explanation:

Let the digit at unit place be  x and that at the decimal place be y.

Therefore the original number will be = 10y + x

When the digits are interchanged then the new number will be 10x + y

According to the question (10x + y) - (10y + x) = 9x - 9y = 9(x - y) = 27 (Given)

Therefore x - y = 27/9 = 3

Therefore x - y = 3 (eq. i)

and x + y = 5 (eq. ii, as provided the sum of the digits equal to 5)

If we add eq.i and eq.ii on both side we will get 2x = 8 and hence x = 4

Putting the value of x at eq.ii we get y = 1.

Hence the original number will be = 10y + x = 10*1+4 = 14