Question

If A.M. of two numbers is 15/2 and their G.M. is 6, then find the two numbers.

(a) 6 and 8

(b) 12 and 3

(c) 24 and 6

(d) 27 and 3

I got this question in unit test.

I want to ask this question from Relationship Between A.M. and G.M. topic in section Sequences and Series of Mathematics – Class 11

Answer 1

The correct option is (b) 12 and 3

The explanation: We know, A.M. of two numbers a and b is (a + b)/2

=> (a + b)/2 = 15/2 => a + b = 15.

Also, G.M. of two numbers a and b is \(\sqrt{ab}\)

=> \(\sqrt{ab}\) = 6 => ab = 36.

=> a(15-a) = 36 => a=3 or 12.

For a=3, b=12.

For a=12, b=3.

So, the two numbers are 3 and 12.