If A1, A2; G1, G2 and H1, H2 be two AMâs, GMâs and HMâs between two quantities, then the value of (G1 G2/H1 H2) is

Question

If A1, A2; G1, G2 and H1, H2 be two AMâs, GMâs and HMâs between two quantities, then the value of (G1 G2/H1 H2) is (A) (A1+A2/H1+H2) (B) (A1-A2/H1+H2) (C) (A1+A2/H1-H2) (D) (A1-A2/H1-H2)

Tardigrade Admin · Accepted Answer

Let the two quantities be a and b. Then a, A1, A2, b are in A P. ∴ A1-a=b-A2 ⇒ A1+A2=a+b ldots(i) Again a, G1, G2, b are in G P. ∴ (G1/a)=(b/G2) ⇒ G1 G2=a b ldots(i i) Also, a, H1, H2, b are in H P. ∴ (1/H1)-(1/a)=(1/b)-(1/H2) ⇒ (1/H2)+(1/H2)=(1/b)+(1/a) ⇒ (H1+H2/H1 H2)=(a+b/a b) ⇒ (H1+H2/H1 H2)=(A1+A2/G1 G2) [using Eqs. (i) and (i i)] ⇒ (G1 G2/H1 H2)=(A1+A2/H1+H2)

Q. If $A_{1}, A_{2}; G_{1}, G_{2}$ and $H_{1}, H_{2}$ be two $A M ’ s$ , $GM ’ s$ and $H M ’ s$ between two quantities, then the value of $\frac{G _{1} G _{2}}{H _{1} H _{2}}$ is

$\frac{A _{1} + A _{2}}{H _{1} + H _{2}}$

$\frac{A _{1} - A _{2}}{H _{1} + H _{2}}$

$\frac{A _{1} + A _{2}}{H _{1} - H _{2}}$

$\frac{A _{1} - A _{2}}{H _{1} - H _{2}}$

Q. If A1​,A2​;G1​,G2​ and H1​,H2​ be two AM’s, GM’s and HM’s between two quantities, then the value of H1​H2​G1​G2​​ is

H1​+H2​A1​+A2​​

H1​+H2​A1​−A2​​

H1​−H2​A1​+A2​​

H1​−H2​A1​−A2​​

Q. If $A_{1}, A_{2}; G_{1}, G_{2}$ and $H_{1}, H_{2}$ be two $A M ’ s$ , $GM ’ s$ and $H M ’ s$ between two quantities, then the value of $\frac{G _{1} G _{2}}{H _{1} H _{2}}$ is

$\frac{A _{1} + A _{2}}{H _{1} + H _{2}}$

$\frac{A _{1} - A _{2}}{H _{1} + H _{2}}$

$\frac{A _{1} + A _{2}}{H _{1} - H _{2}}$

$\frac{A _{1} - A _{2}}{H _{1} - H _{2}}$