Question

the no.consists of two digits.when it is divided by the sum of its digits,the quotient is 6 with no remainder. when the number is diminished by 9, the digits are reversed.Find the number

Answer 1

Let the number be xy

When it is divided by the sum of its digits,the quotient is 6 with no remainder:

(10x + y)/(x+y) = 6

10x + y = 6x + 6y

4x = 5y

x = 5/4 y -------- (i)

When the number is diminished by 9, the digits are reversed:

10x + y - 9 = 10y + x

9x - 9y = 9

x - y = 1 ------ (ii)

Solving (i) and (ii) simultaneously;

x - y = 1

but, x = 5/4 y

So,

5/4 y - y = 1

y/4 =  1

y = 4

x = 5/4 y

x = 5/4 (4) = 5

So, the number = 54