Question

a two-digit number is such that the sum of its digits is 8. If 54 is subtracted from the number, its
digits are reversed. Find the number.​

Answer 1

71

Let the unit digit be x and ten's digit be y

Original number :- 10y + x Reversed number:- 10x + y

x+y=8

x = 8-y ......... (i)

10y + x - 54 = 10x + y

10y - y + x - 10x = 54

9y - 9x = 54

y - x = 6 (ii)

Putting the value from (i) in (ii)

y-x = 6

y-(8-y)=6

y-8+y=6

2y = 6 + 8

2y = 14

y = 7

Putting the value of y in (i)

x=8-y

x=8-7

x = 1

Original number :- 10y + x

10 × 7 + 1

70 + 1

71