Advertisement

### Question

When a two digit number is reversed and added to itself we get 110. The product of the digits of that number is 21. What is the number?

**A**

73.

**B**

74.

**C**

72.

**D**

75.

**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 110 = 11 × (a + b) ⇒ $a + b = 110 / 11 = 10$, so the digits are $a$ and $10 - a$. We are given their product as a × (10 - a) = 21, which is a quadratic expression that can be simplified to $(a - 7) × (3 - a) = 0$. So the number could be 73 or 37.