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

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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.

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Here, IL : IP = 4 : 5;

IF = 150,

IP = ?

∴ $\cfrac{I_L}{I_P}=\frac{4}{5}$

∴ $I_L=\cfrac{4}{5}\,I_p$

Now, I$=\sqrt{I_L \times I_p}$

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

∴ $(150)^2=\frac{4}{5} {I_p}^2$

∴ $\frac{22500×5}{4} = {I_P}^2$

∴ IP2 = 28125

∴ IP = 167.71