Question
A two-digit number has a sum of its digits equal to 11.
Additionally, if 54 is subtracted from this number, the resulting number has its digits reversed. What is 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 = 11 --------- (I)
And, 10b + a - 54 = 10a + b
Or, 9b - 9a = 54
Or, b - a = 6 ---------- (II)
On adding equation I and II,
We get, a + b + b - a = 11 + 6
Or, 2b = 17
Or, 'b' = 8
On putting value of 'b' in equation I,
We get, 8 + a = 11
Or, 'a' = 3
Required number = 10 × 8 + 3 = 83
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