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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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1 Answer

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Here, IL : IP = 4 : 5;

IF = 150,

IP = ?

\(\therefore \frac{I_L}{I_P} = \frac 45\)

\(\therefore{I_L} = \frac 45{I_P}\)

Now, \(I_F = \sqrt{I_L \times I_P}\)

\(150 = \sqrt{\frac 45 I_P \times I_P}\)

\( (150)^2 = {\frac 45 {I_P}^2}\)

\(\frac{22500\times 5}{4} = {\frac 45 {I_P}^2}\)

\({I_P}^2 = 28125\)

\(\therefore {I_P}= 167.71\)

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