If the sum of two numbers is 41 and their product is 400. Then the numbers are ……………… 

Correct option is (C) 25, 16

Let the numbers are a and b.

Sum of numbers is 41.

\(\therefore\) a+b = 41        __________(1)

And product of the number is 400.

\(\therefore\) ab = 400        __________(2)

Now, \((a-b)^2=(a+b)^2-4ab\)

\(=41^2-4\times400\)

= 1681 - 1600

= 81 \(=9^2\)

\(\Rightarrow\) a - b = 9        __________(3)

By adding equations (1) & (3), we get

(a+b) + (a - b) = 41+9

\(\Rightarrow\) 2a = 50

\(\Rightarrow\) a = \(\frac{50}2\) = 25

\(\therefore\) b = 41 - a         (From (1))

= 41 - 25 = 16

Hence, required numbers are 25 and 16.

Correct option is C) 25, 16