Question
A two-digit number has digits summing up to 10. On subtracting 36 from the number, the digits get interchanged. What is the original number?
Solution
ATQ,
Let the ones digit = 'a', tens digit = 'b'
Number = 10b + a, Reversed = 10a + b
a + b = 10 --------- (I)
10b + a - 36 = 10a + b
⇒ 9b - 9a = 36
⇒ b - a = 4 --------- (II)
Add (I) and (II):
a + b + b - a = 10 + 4
⇒ 2b = 14 ⇒ b = 7
Then a = 3
Required number = 10 × 7 + 3 = 73
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