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### Question

The difference between a two digit number and the one obtained by reversing its digits is 81. If one of the digits is 5, what is the other?

**A**

Cannot exist.

**B**

5.

**C**

6.

**D**

7.

**Soln.**

**Ans: a**

Let the numbers be a and b. ab = 10a + b, and ba = 10b + a. The difference is 10a + b - (10b + a) = 9(a - b). It is given that 9(a - b) = 81, ⇒ a - b = $81/9$ = 9, ⇒ the difference between the digits is 9. If one of the digits is 5, the other cannot be determined.