Question
Sum of digits of a two-digit number is 9. When 27 is
subtracted from the number, its digits get reversed. Find the original number.Solution
ATQ,
Let ones and tens digit of the number be 'a' and 'b' respectively. So, original number = 10b + a Reverse number = 10a + b So, a + b = 9 --------- (I) And, 10b + a - 27 = 10a + b Or, 9b - 9a = 27 Or, b - a = 3 ---------- (II) On adding equation I and II, We get, a + b + b - a = 9 + 3 Or, 2b = 12 Or, 'b' = 6 On putting value of 'b' in equation I, We get, 6 + a = 9 Or, 'a' = 3 Required number = 10 × 6 + 3 = 63
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