Compute both indices, then check each commodity's share of the total price rise in each method.

(a) $\Sigma p_0=65$, $\Sigma p_1=90$; $P_{01}=\dfrac{90}{65}(100)=138.46$. Of the total rise of 25, Z alone contributes 15 (60%), despite being bought in the smallest quantity. …

1. Simple Aggregate Method.

   $\Sigma p_0=10+50+5=65, \qquad \Sigma p_1=15+55+20=90$

   $P_{01}=\dfrac{90}{65}\times100=138.46$

   The total price rise here is $90-65=25$. Splitting this by commodity: X contributes $15-10=5$, Y contributes $55-50=5$, and Z contributes $20-5=15$ — so Z ALONE accounts for $\dfrac{15}{25}=60\%$ of the entire measured rise, even though Z is bought in the smallest quantity of the three (only 1 unit).
2. Weighted Aggregate Method (weight $w=q_0$):

   $\Sigma p_0 q_0 = 10(20)+50(2)+5(1) = 200+100+5=305$

   $\Sigma p_1 q_0 = 15(20)+55(2)+20(1) = 300+110+20=430$

   $P_{01}=\dfrac{430}{305}\times100=140.98$ …

It is tempting to think the commodity with the LARGEST PERCENTAGE price increase (here Z, which quadrupled) should dominate any price index — but a price index measures the change in what is actually BOUGHT, so a large percentage rise on a tiny quantity has little real eff …