If the average of two numbers is 13 and the square root of their product is 12, then the difference between the numbers is:

Options:
a) 8
b) 18
c) 10
d) 12

Solution:

Let the two numbers are = a and b
Average of number = $ \frac{a+b}{2}=13$
a+b =26
Product = $ \sqrt{a \times b} =12$
a x b =144

Formula = $ (a + b)^2= a^2+b^2 + 2ab$ and $ (a – b)^2= a^2+b^2 – 2ab$
$ (a + b)^2 – (a-b)^2= (a^2+b^2 + 2ab) – (a^2+b^2-2ab) $
$ (a + b)^2 – (a-b)^2 = 4ab$
Put the value of a+b and a x b
=> $ (26)^2 – (a-b)^2 = 4 \times 144$
=> $ (a-b)^2 = 676-576 = 100 = 10^2$
=> (a-b) = 10

Ans: 10