Given that \(\sum p_0q_0=800\), \(\sum p_0q_1=900\), \(\sum p_1q_0=1000\), \(\sum p_1q_1=1200\) where subscripts 0 and 1 refer to base year and current year respectively. The Laspeyres’ Index number is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 125
Laspeyres’ index weights the prices by the base-year quantities \(q_0\):
\( \displaystyle P_{01} = \frac{\sum p_1q_0}{\sum p_0q_0}\times 100 \)
\( \displaystyle = \frac{1000}{800}\times 100 = 125 \)
Why the other options are incorrect
Option (2) 133.33 — Incorrect. This is \(\frac{1200}{900}\times 100\), Paasche’s index (current-year quantities \(q_1\)).
Option (3) 150 — Incorrect. This is \(\frac{\sum p_1q_1}{\sum p_0q_0}\times 100 = \frac{1200}{800}\times 100\), the value index, not a price index.
Option (4) 75 — Incorrect. This is \(\frac{900}{1200}\times 100\); the base-year quantities cost 1000 at current prices against 800 at base prices, so the index must be above 100.
Note: This topic was not in the CUET 2026 syllabus.