38. The sum of the digits of a 2-digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number. Plz give whole calculation.
Answers
Answer:
x = 3 and y = 9
Step-by-step explanation:
Let the number's ten's place be x, unit's place be y
Original number: 10x + y
Number after reversing digits: 10y + x (Unit's place becomes ten's place and vice versa)
Also, given that new number after reversing digits is greater than the original number by 54
So, 10x + y + 54 = 10y + x
⇒ 10x + y + 54 - 10y - x = 0
⇒ 10x - x + y - 10y + 54 = 0
⇒ 9x - 9y + 54 = 0
⇒ 9 ( x - y + 6 ) = 0
⇒ x - y + 6 = 0
⇒ 0 = x - y + 6
⇒ 0 + y = x + 6
⇒ y = x + 6 -----------------------------> (1)
Also given, sum of digits, i.e., x + y = 12
By substituting the value of y from (1) in the above equation,
x + ( x + 6 ) = 12
⇒ x + x + 6 = 12
⇒ 2x = 12 - 6
⇒ 2x = 6
⇒ x = 6/2
⇒ x = 3
Again, from (1),
y = x + 6
= 3 + 6
= 9
∴ x = 3 and y = 9
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