CA Foundation P3 · Chapter 18

Index Numbers MCQs with Answers

9 multiple-choice questions on Index Numbers for CA Foundation P3 Quantitative Aptitude. Try each one before revealing the answer and explanation.

1. Question 1

   The sum of base-year prices of a group of commodities is ₹250 and the sum of current-year prices is ₹300. The simple aggregative price index is:

   • A) 83.33
   • B) 150
   • C) 120
   • D) 50
   Show answer & explanation

   Answer: C) 120

   Simple aggregative index = (Σp₁/Σp₀) x 100 = (300/250) x 100 = 120. Inverting the ratio gives 83.33, and the difference 300 − 250 = 50 is not an index.

2. Question 2

   Using the data below, Laspeyres' price index is (to two decimals): Item A: p₀ = 10, q₀ = 5, p₁ = 12, q₁ = 6 Item B: p₀ = 8, q₀ = 10, p₁ = 10, q₁ = 8 Item C: p₀ = 5, q₀ = 8, p₁ = 6, q₁ = 10

   • A) 122.35
   • B) 121.84
   • C) 81.73
   • D) 124.71
   Show answer & explanation

   Answer: A) 122.35

   Laspeyres uses base-year quantities: Σp₁q₀ = 60 + 100 + 48 = 208 and Σp₀q₀ = 50 + 80 + 40 = 170. Index = (208/170) x 100 = 122.35. 121.84 is the Paasche index and 81.73 is the inverted ratio (170/208 x 100).

3. Question 3

   Using the data below, Paasche's price index is (to two decimals): Item A: p₀ = 10, q₀ = 5, p₁ = 12, q₁ = 6 Item B: p₀ = 8, q₀ = 10, p₁ = 10, q₁ = 8 Item C: p₀ = 5, q₀ = 8, p₁ = 6, q₁ = 10

   • A) 122.35
   • B) 124.71
   • C) 121.84
   • D) 82.08
   Show answer & explanation

   Answer: C) 121.84

   Paasche uses current-year quantities: Σp₁q₁ = 72 + 80 + 60 = 212 and Σp₀q₁ = 60 + 64 + 50 = 174. Index = (212/174) x 100 = 121.84. 122.35 is Laspeyres', and 124.71 wrongly divides Σp₁q₁ by Σp₀q₀ (212/170).

4. Question 4

   Laspeyres' price index is 125 and Paasche's price index is 120. Fisher's ideal index is (to two decimals):

   • A) 122.50
   • B) 245.00
   • C) 120.00
   • D) 122.47
   Show answer & explanation

   Answer: D) 122.47

   Fisher's index is the geometric mean of Laspeyres' and Paasche's indices: √(125 x 120) = √15,000 = 122.47. 122.50 is the arithmetic mean (Bowley's index), not Fisher's.

5. Question 5

   Which index number satisfies both the time reversal test and the factor reversal test?

   • A) Laspeyres' index
   • B) Fisher's ideal index
   • C) Paasche's index
   • D) Simple aggregative index
   Show answer & explanation

   Answer: B) Fisher's ideal index

   Fisher's index, √(L x P), satisfies both the time reversal test (P₀₁ x P₁₀ = 1) and the factor reversal test (P₀₁ x Q₀₁ = V₀₁). Laspeyres' and Paasche's indices satisfy neither of these tests.

6. Question 6

   The link relatives of prices for three successive years (each on the previous year as 100) are 110, 105 and 120. Taking the year before the first as base (= 100), the chain index for the third year is:

   • A) 135.0
   • B) 111.67
   • C) 138.6
   • D) 126.0
   Show answer & explanation

   Answer: C) 138.6

   Chain index = product of link relatives / 100² = (110 x 105 x 120)/10,000 = 1.10 x 1.05 x 1.20 x 100 = 138.6. Adding the percentage rises (10 + 5 + 20 = 35) gives 135, and the simple average of the relatives gives 111.67.

7. Question 7

   On an old base, the index numbers for years X and Y are 150 and 180. If the base is shifted to year X, the new index for year Y is:

   • A) 120
   • B) 130
   • C) 83.33
   • D) 30
   Show answer & explanation

   Answer: A) 120

   Shifted index = (old index of Y / old index of X) x 100 = (180/150) x 100 = 120. Subtracting 50 from 180 gives 130, and inverting gives 83.33.

8. Question 8

   A worker's money wage is ₹30,000 per month and the consumer price index (base = 100) is 150. His real wage in base-year prices is:

   • A) ₹45,000
   • B) ₹30,150
   • C) ₹25,000
   • D) ₹20,000
   Show answer & explanation

   Answer: D) ₹20,000

   Real wage = (money wage / price index) x 100 = (30,000/150) x 100 = ₹20,000. Multiplying by the index instead of dividing gives ₹45,000.

9. Question 9

   The price relatives of three items are 120, 150 and 110, with weights 5, 2 and 3 respectively. The weighted index of price relatives is:

   • A) 126.67
   • B) 123
   • C) 133
   • D) 41
   Show answer & explanation

   Answer: B) 123

   Weighted index = ΣwP/Σw = (5 x 120 + 2 x 150 + 3 x 110)/(5 + 2 + 3) = (600 + 300 + 330)/10 = 1,230/10 = 123. The simple average (380/3) is 126.67.