Question

A number consisting of two digits is seven times the sum.of it's digits. when 27 is subtract from the number, the digits are reversed. find the number.

Answer 1

let no be (x*10)+y

where x is the first digit and y is the units digit.[13 can be expressed as 10*1+3]

10x+y = 7(x+y)

10x + y = 7x + 7y

3x = 6y ⇒ x = 2y

now the second statement:

if the digits are reversed (i.e.) 10y+x = 10x+y-27

now put x = 2y

9y = 9(2y)-27

27 = 9y⇒y = 3 and  x = 6

the number is 63