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Question

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

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Solution

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

A = 25

a+b2=25

a+b=50 ..........(i)

Also, G = 20

ab=20

ab=400 ..........(ii)

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

(50b)b=400

b250b+400=0

b210b40b+400=0

b(b10)40(b10)=0

(b10)(b40)=0

b=10,40

If b = 10, then, a = 400

And, if b = 40, then a = 10

Thus, the two numbers are 10 and 40.


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