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