This is a direct application of the Weighted Aggregate Method, using the base-year quantity $q_0$ as the weight $w$ for every commodity.

$\Sigma p_0 w = 30(10)+25(8)+40(5)+120(2) = 300+200+200+240 = 940$.

$\Sigma p_1 w = 45(10)+35(8)+55(5)+150(2) = 450+280+275+300 = 1305$.

$P_{01}=\dfrac{1305}{940}\times100 = 138.83$.

The Weighted Aggregate Method uses the base-year quantity $q_0$ as the weight $w$ for every commodity:

First compute $p_0 w$ for every commodity (base-year price times base-year quantity):

Then compute $p_1 w$ for every commodity, using the SAME weight $q_0$ as above but the current-year price:

Substituting:

Notice this weighted figure (138.83) is higher than the Simple Aggregate figure from Worked Example 1 (132.56) — here it happens because Rice and Sugar, which the household buys in the largest quantities (10 kg and 5 kg), both had comparatively large price rises.

The most frequent error is using a DIFFERENT weight for a commodity's current-year price than for its base-year price (for instance, mixing up which row a quantity belongs to) — the same weight $q_0$ must multiply both $p_0$ and $p_1$ for a given commodity.