Question

a 2-digit number is 5 times the sum of its digits.If 9 is added to thr number,its digits are reversed. Find the number

Answer 1

let the first digit be x
& the last digit is y
then 10x+y=5(x+y)
or 10x-5x+y-5y=0
or 5x=4y
or x=(4/5)y..................(1)

again
10x+y+9=10y+x
or 9y-9x=9
or y-x=1......................(2)
putting the value of x in(1) to (2)
y-(4/5)y=1
or y=5
putting the value of y in (1)
x=(4/5)*5
or x=4

x=4
y=5....................(ans)

Answer 2

Answer: Let the first digit be x

And second digit be y

- According to question

10x + y = 5(x+y)

10x + y = 5x + 5y

Therefore,

x = 4/5y. ......(1)

Now,

10y + x + 9 = 10x + 9y

9y - 9x = 9

y - x = 1. .......(2)

Putting value of x from (1) in (2) , we get

y - 4/5y = 1

5y - 4y = 5

y = 5

Therefore

x = 4/5 . 5

x = 4