Question

Find the two numbers whose A.M. is 25 and GM is 20.

Answer 1

Let A.M. and G.M. between the two numbers a and b be A and G, respectively.

A = 25

$\Rightarrow \frac{a+b}{2}=25$

$\Rightarrow a+b=50$ ..........(i)

Also, G = 20

$\Rightarrow \sqrt{ab}=20$

$\Rightarrow ab=400$ ..........(ii)

Now, putting the value of a in (ii):

$\Rightarrow (50-b)b=400$

$\Rightarrow b^2-50b+400=0$

$\Rightarrow b^2-10b-40b+400=0$

$\Rightarrow b(b-10)-40(b-10)=0$

$\Rightarrow (b-10)(b-40)=0$

$\Rightarrow b=10,40$

If b = 10, then, a = 400

And, if b = 40, then a = 10

Thus, the two numbers are 10 and 40.