Question

give a step by step explaination​

Answer 1

Answer:

Original number = 81

Step-by-step explanation:

Let the number have the digits x and y.

So the Original number is 10x+ y.

From first statement:

(10x + y) / (x + y) = 9

⇒ 10x + y = 9x + 9y

⇒ x - 8y = 0    ... (i)

Since x and y are single digit numbers, solutions of above equation are

(x, y) = (0, 0), (8, 1).

Omitting (0, 0) as x and y are not distinct, only possible solution is (8, 1).

So x = 8, y = 1 and the original number is 81.

And sum of their digits is 9.

Validating second statement:

Number obtained by reducing tenth digit by 4x unit digit = 10(x-4y) + y

∴  we need to check if (10(x-4y) + y ) / (x + y) leaves remainder 5.

that is, (81 - 40) / 9 = 41 /9 = 4 5/9.

Here 5 is the remainder left !