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Question

ab is a two digit number whose sum of the digits is 12 . The number obtained by subtracting ab from the number obtained after reversing the digits is 54. Find the number.

A
39
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B
93
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C
84
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D
48
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Solution

The correct option is A 39
Let the two digit number be ab = 10a + b and its reverse will be ba = 10b + a.
Now, ba - ab
= 10b + a - (10a + b)
= 10b + a - 10a - b
= 9b - 9a
= 9 (b - a)

Given 9 (b - a) = 54
b - a = 6
and b + a = 12 (given)
b+b+6=12 (substituting value of a)
2b = 18
b = 9
and a = 3

So, the number ab is 39.

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