Question

a number between 10 and 100 is 5 times the sum of its digits if9 be added to it the digits are reserved find the number

Answer 1

Take the tens digit as x and ones digit as y
so the number formed is 10x+y
acc.to the question.. and 10x+y=5(x+y)
5x=4y so 5x-4y=0 this equation no.1

now,
reverse of number will be 10y+x
acc. to the question..10x+y+9=10y+x
and 10x+y-10y+x=-9. Solve it to get 9x - 9y=-1
or x-y=-1 This is equation no. 2
solve both equations (Simultaneous linear equation)
to get x=4 and y=5
no.is 10x+y=40+5
45 is the number