Question

If A1, A2; G1, G2; and H1, H2 are two AMs, GMs and HMs between two quantities, then the value of G1G2H1H2 is

• A. (A) A1+A2H1+H2
• B. (B) A1−A2H1+H2
• C. (C) A1+A2H1−H2
• D. (D) A1−A2H1−H2

Answer 1

Answer: (A)

(A) A1+A2H1+H2

Answer 2

Explanation:
Let the two quantities be a and b. Then a,A1 A2,b are in AP∴A1−a=b−A2⇒A1+A2=a+bAgain a,G1,G2,b are in GP∴G1a=bG2⇒G1G2=abAlso, a,H1,H2,b are in HP.∴1H1−1a=1b−1H2⇒1H1+1H2=1b+1a⇒H1+H2H1H2=a+bab⇒H1+H2H1H2=A1+A2G1G2[using Eqs.(i) and G1G2H1H2=A1+A2H1+H2