Compute both index numbers using their respective formulae, then compare which commodity dominates each one.

1. $\Sigma p_0=5+50=55$, $\Sigma p_1=10+55=65$; $P_{01}=\dfrac{65}{55}(100)=118.18$.
2. $\Sigma p_0 q_0=5(30)+50(1)=200$, $\Sigma p_1 q_0=10(30)+55(1)=355$; $P_{01}=\dfrac{355}{200}(100)=177.5$. …

1. Simple Aggregate Method.

   $\Sigma p_0 = 5+50=55, \qquad \Sigma p_1=10+55=65$

   $P_{01}=\dfrac{65}{55}\times100=118.18$

2. Weighted Aggregate Method (weight $w=q_0$):

   $\Sigma p_0 q_0 = 5(30)+50(1) = 150+50=200$

   $\Sigma p_1 q_0 = 10(30)+55(1) = 300+55=355$

   $P_{01}=\dfrac{355}{200}\times100=177.5$

   Why the two differ so sharply: in the Simple Aggregate Method, every commodity's raw price counts once, with no regard to quantity — and Q's base price of Rs. 50 makes up $\dfrac{50}{55}=91\%$ of $\Sigma p_0$, even though the household buys only 1 unit of Q against 30 units of P. So the Simple Aggregate index is dominated by Q's modest 10% price rise (Rs. 50 to Rs. 55), and P's price DOUBLING (Rs. 5 to Rs. 10) barely moves the result, because P's base price is numerically small. The Weighted Aggregate Method corrects this exactly: multiplying by $q_0$ makes P's true economic weight (30 units) count 30 times over, so the inde …

A common mistake is assuming the Simple Aggregate Method is 'wrong' in some arithmetic sense — it is arithmetically correct, but conceptually unsuited to data where commodities are consumed in very different quantities; …