Question

A number consisting of two digits is seven times the sum of its digits.When 27 is subtracted from the number,the digits are reversed.Find the number.

Answer 1

Let x be the digit at tens place and y be the digit at once place
So according to question

7(x+y)=10x+y
3x-6y=0
x-2y=0................(1)

Also when 27 is subtracted from number

10x+y-27=10y+x

9x-9y=27
x-y=3.............(2)

Subtracting both equations
-y=-3
y=3
Putting value of y in eq 2 we get
x=6

Putting the value of x= 6 and y=3 in 10x +1y the original number we have

10 (6) + 1 (3) = 60 + 3= 63

So the number is 63