Question
The sum of the digits of a two-digit number is 9. If 27 is subtracted from the number, its digits switch their places. What is the number?
Solution
ATQ,
Let the unit digit be 'a' and tens digit be 'b'.
Original number = 10b + a
Reversed number = 10a + b
Given:
a + b = 9 --------- (I)
10b + a - 27 = 10a + b
⇒ 9b - 9a = 27
⇒ b - a = 3 --------- (II)
Add equations (I) and (II):
a + b + b - a = 9 + 3
⇒ 2b = 12 ⇒ b = 6
Then a = 9 - 6 = 3
Required number = 10 × 6 + 3 = 63
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