Question

A two digit number is such that 4 times the units digit exceeds the tens digit by1. If the digits are reversed, the number formed is decreased by 45. Find the number.

Answer 1

let the number be xy
4y − x =1......(i)
10x+y−(10y+x) =45
10x+y−10y−x =45
 9x−9y =45......(ii)        
From (i) x=4y−1, subst in (ii)
9(4y−1)−9y =45
36y−9−9y =45
   27y = 54
       y=2                     
x = 4 × 2−1
   =8−1 =7
The no. is 72