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### Question

When a two digit number is reversed and added to itself we get 143. The product of the digits of that number is 36. What is the number?

**A**

49.

**B**

50.

**C**

48.

**D**

51.

**Soln.**

**Ans: a**

Let the number be ab. When it is reversed and added to itself we get (10a + b) + (10b + a) = 11 × (a + b). We are given 143 = 11 × (a + b) ⇒ $a + b = 143 / 11 = 13$, so the digits are $a$ and $13 - a$. We are given their product as a × (13 - a) = 36, which is a quadratic expression that can be simplified to $(a - 4) × (9 - a) = 0$. So the number could be 49 or 94.