If the sum of two numbers be multiplied by each number separately,

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If the sum of two numbers be multiplied by each number separately, the products so obtained are 247 and 114. The sum of the numbers is

1. 19
2. 20
3. 21
4. 23

Correct Option: A

Let the numbers be x and y.
∴ x (x + y) = 247
and y (x + y) = 114
⇒ x² = 247 and xy + y²
= 114
On adding;
x² + xy + xy + y² = 247 + 114
⇒ x² + 2xy + y² = 361
⇒ (x + y)² = 19² ⇒ x + y = 19