Question

If the ratio of Laspeyre’s and Paasche’s index number is 4:5 and Fisher’s index number is 150, find Paasche’s index number.

Answer 1

Here, I_L : I_P = 4 : 5;

I_F = 150,

I_P = ?

∴ \(\cfrac{I_L}{I_P}=\frac{4}{5}\) 

∴ \(I_L=\cfrac{4}{5}\,I_p\)

Now, I_{F \(=\sqrt{I_L \times I_p}\)}

∴ 150 = \(\sqrt{\frac{4}{5} I_p \times I_p}\)

∴ \((150)^2=\frac{4}{5} {I_p}^2\)

∴ \(\frac{22500×5}{4} = {I_P}^2\)

∴ I_P² = 28125

∴ I_P = 167.71