The sum of the squares of two positive integers is 100 and

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The sum of the squares of two positive integers is 100 and the difference of their squares is 28. The sum of the numbers is :

1. 12
2. 13
3. 14
4. 15

Correct Option: C

Let the numbers be x and y.
Then,
x² + y² = 100 ...(i)
x² – y² = 28 ...(ii)
On adding,
2x² = 128
⇒ x² = 64 ⇒ x = 8
From equation (i),
64 + y² = 100
⇒ y² = 36 ⇒ y = 6
∴ Required sum
= 8 + 6 = 14