Question

The sum of the digits of a 2-digit number is 10. If we reverse the digits, the new number will be 54
more than the original number. What is the original number?
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Answer 1

Answer:

let the unit digit =x

then tens digit=y

so number is 10y+x

x+y=10

if digits are reversed then no is,-

10x+y

now, 10x+y= 10y+x+54

9x-9y=54

divide by 9 on both sides

x-y= 6

x+y=10

from these two equations x=8, y=2

now the original no - 10×2+8 = 28