The price of a basket of three essential items in the base year was Rs. 10, Rs. 20 and Rs. 15. In the current year, the same three items cost Rs. 12, Rs. 25 and Rs. 18. Compute the Simple Aggregative Price Index for the current year, and state whether prices have risen or fallen

Question

The price of a basket of three essential items in the base year was Rs. 10, Rs. 20 and Rs. 15. In the current year, the same three items cost Rs. 12, Rs. 25 and Rs. 18. Compute the Simple Aggregative Price Index for the current year, and state whether prices have risen or fallen on average.

Accepted Answer

**Base-year total:**
$$\sum P_{0}=10+20+15=Rs.\,45$$

**Current-year total:**
$$\sum P_{1}=12+25+18=Rs.\,55$$

**Simple Aggregative Price Index:**
$$	ext{Price Index}=\dfrac{\sum P_{1}}{\sum P_{0}}	imes100=\dfrac{55}{45}	imes100=122.22$$

**Verification via percentage change:** the percentage change formula applied to the two totals gives $\dfrac{55-45}{45}	imes100=\dfrac{10}{45}	imes100=22.22\%$, which is exactly the amount by which the index (122.22) exceeds 100 — the two calculations are consistent, since an index of 122.22 means prices are 22.22% higher than the base year by construction. …

Q.The price of a basket of three essential items in the base year was Rs. 10, Rs. 20 and Rs. 15. In the current year, the same three items cost Rs. 12, Rs. 25 and Rs. 18. Compute the Simple Aggregative Price Index for the current year, and state whether prices have risen or fallen on average.

Concept understanding — Index Numbers and Percentage Change

Q.The price of a basket of three essential items in the base year was Rs. 10, Rs. 20 and Rs. 15. In the current year, the same three items cost Rs. 12, Rs. 25 and Rs. 18. Compute the Simple Aggregative Price Index for the current year, and state whether prices have risen or fallen on average.

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