Question

Two digits are a number. When this number is divided by the sum of digits, the quotient is 6 and there is nothing left. If 9 is subtracted from the number, then the digits of the number are reversed. Find the number.​

Answer 1

Answer:-

Let the number be (10x + y).

Given:

If the number is divided by the sum of the digits , the quotient obtained is 6.

→ (10x + y)/(x + y) = 6

→ 10x + y = 6(x + y)

→ 10x + y = 6x + 6y

→ 10x - 6x = 6y - y

→ 4x = 5y

→ x = 5y/4 -- equation (1)

And,

If 9 is subtracted from the number, the digits are reversed.

→ (10x + y) - 9 = 10y + x

→ 10x - x = 10y - y + 9

→ 9x = 9y + 9

→ 9(x) = 9(y + 1)

→ x = y + 1

Put the value of x from equation (1) here.

→ 5y/4 = y + 1

→ 5y = 4(y + 1)

→ 5y = 4y + 4

→ 5y - 4y = 4.

→ y = 4

Substitute y value in equation (1).

→ x = 5(4)/4

→ x = 5

The number = 10(5) + 4 = 54.

Hence, the number is 54.