CA FOUNDATION: QUANTITATIVE APTITUDE · INDEX NUMBERS

Index numbers: simple aggregative and Laspeyres

Simple aggregative P01 = Σp1 ÷ Σp0 × 100. Laspeyres P01 = Σp1q0 ÷ Σp0q0 × 100 (base-year quantities).

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Worked examples

Example 1 · level 1

Prices (₹) — Tur dal (kg): base 130, current 155; Rice (kg): base 250, current 270; Sugar (kg): base 255, current 270. Find the simple aggregative price index (base = 100), two decimals.

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Σp0 = 130 + 250 + 255 = 635.
Σp1 = 155 + 270 + 270 = 695.
P01 = 695 ÷ 635 × 100 = 109.45.

Answer: 109.45

Example 2 · level 2

Prices (₹) — Rice (kg): base 290, current 315; Wheat (kg): base 35, current 35; Onion (kg): base 75, current 115; Mustard oil (litre): base 220, current 220. Find the simple aggregative price index (base = 100), two decimals.

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Σp0 = 290 + 35 + 75 + 220 = 620.
Σp1 = 315 + 35 + 115 + 220 = 685.
P01 = 685 ÷ 620 × 100 = 110.48.

Answer: 110.48

Example 3 · level 3

Base-year quantity q0 and prices p0 → p1 (₹): Tur dal (kg): q0 6, p0 140, p1 140; Rice (kg): q0 2, p0 285, p1 305; Onion (kg): q0 1, p0 135, p1 165; Mustard oil (litre): q0 6, p0 190, p1 205. Find Laspeyres’ price index, two decimals.

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Σp0q0 = 140×6 + 285×2 + 135×1 + 190×6 = 2,685.
Σp1q0 = 140×6 + 305×2 + 165×1 + 205×6 = 2,845.
P01 = 2,845 ÷ 2,685 × 100 = 105.96.

Answer: 105.96