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Practice Exercise · Q3
Q.

Taking 1995 as base year calculate relative index number for the years 1997-2005

Year199519971999200120032005
Price (in ₹)121413202521
CBSENCERTSubjective· 3mImportance★★★★★est
35% · 14/40 Questions
✓ Free question

Using pn12×100\dfrac{p_n}{12}\times100, the price-relative index numbers are 116.67, 108.33, 166.67, 208.33 and 175.00 for 1997, 1999, 2001, 2003, 2005.

In=pnp0×100I_n=\dfrac{p_n}{p_0}\times100

where p0=₹12p_0=₹12 is the 1995 base price and pnp_n is the price of year nn.

Working table

YearPrice pnp_n (₹)pn12×100\dfrac{p_n}{12}\times100Index
1995121212×100\frac{12}{12}\times100100.00
1997141412×100\frac{14}{12}\times100116.67
1999131312×100\frac{13}{12}\times100108.33
2001202012×100\frac{20}{12}\times100166.67
2003252512×100\frac{25}{12}\times100208.33
2005212112×100\frac{21}{12}\times100175.00
  1. Base price p0=₹12p_0=₹12 (1995), so its index is 100100.
  2. 1997: 1412×100=1.16667×100=116.67\dfrac{14}{12}\times100=1.16667\times100=116.67.
  3. 1999: 1312×100=1.08333×100=108.33\dfrac{13}{12}\times100=1.08333\times100=108.33.
  4. 2001: 2012×100=1.66667×100=166.67\dfrac{20}{12}\times100=1.66667\times100=166.67.
  5. 2003: 2512×100=2.08333×100=208.33\dfrac{25}{12}\times100=2.08333\times100=208.33.
  6. 2005: 2112×100=1.75000×100=175.00\dfrac{21}{12}\times100=1.75000\times100=175.00.
  7. Self-check: the 2001 price (₹20₹20) is 2012≈1.67\tfrac{20}{12}\approx1.67 times the base, matching the index 166.67166.67.
✓Final answer

Price relatives (base 1995 = 100): 1997 = 116.67, 1999 = 108.33, 2001 = 166.67, 2003 = 208.33, 2005 = 175.00.

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