Question

The sum of the digit of a two digit number is 7 if the digit are reversed the number formed is 9 less than the original number. Find the number

Answer 1

solution:

condition 1 : The sum of the digit of a two digit number is 7.
let the number in tens digit be x,
let the number in ones digit be y,
 
so, x+y=7..(i)

condition 2:If the number 's digit is reversed it is 9 less than the original number,

the original number = 10x+y
the number reversed =10y+x

10x+y=10y+x+9
10x-x+y-10y=9
9x-9y=9=> x-y=1..(ii)

(i)+(ii)=>(x+y)+(x-y)=7+1
                             2x =8
                               x=4

(i)=> x+y=7
         4+y=7
             y=7-4
             y=3

∴The original number is 10x+y=10(4)+3=40+3=43

                          Hope it Helps!!