Divide 16 into 2 parts such the twice the square of the larger part exceeds the square of the smaller part by 164.

Let the smaller part be x. Then the larger part = 16 − x.
According to question , we have
2( larger part )² - ( smaller part )² = 164
Now , 2( 16 - x )² - x² = 164
⇒ 2( 256 + x² - 32x ) - x² = 164
⇒ x² - 64x + 348 = 0
⇒ x² - 6x - 58x + 348 = 0
⇒ x(x - 6) - 58(x - 6) = 0
⇒ (x - 6) (x - 58)
x = 6 or x = 58
But m = 58 is not possible, since sum of the two parts is 16
∴ smaller part ( x ) = 6,
∴ other part = 16 - x = 16 - 6 = 10.
Hence , required answer will be option A .