Question

A certain number consists of two digits .the number is equal to five times the sum of its digits .if you add 9 to the number ,the order of its digits is reversed.what is the number

Answer 1

Let unit place digit be y and tens place digit be x,

Thus, the number becomes: 10x+y and the reverse of the number is: 10y+x

Now, according to question,

the number is equal to five times the sum of its digits

10x+y = 5(x+y)

10x+y = 5x+5y

5x=4y

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

Also, given, if you add 9 to the number ,the order of its digits is reversed

10x+y+9 = 10y+x

9x = 9y-9

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

Solving equation (i) and equation (ii),

x = 4, y = 5

Thus, the number is: 45