# Discussion of Question with ID = 006 under Problems-on-Numbers

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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.