The following table shows Net National Income (in Lac Crore) and Per capita…
2023
The following table shows Net National Income (in Lac Crore) and Per capita Net National Income (in thousand) of India during the 5 year period from the year 2015-16 to 2019-20. Based on the data in the table, answer the questions that follow:
Year | Net National Income (in Lac Crore rupees) | Per capita Net National Income (in thousand rupees) |
|---|---|---|
2015-16 | 122 | 95 |
2016-17 | 136 | 105 |
2017-18 | 151 | 115 |
2018-19 | 167 | 126 |
2019-20 | 177 | 132 |
Assuming that the per capita Net National Income grows beyond the year 2019-20 at the average annual rate of increase (%) of the period (2015-16 to 2019-20), what will be its value (in thousand ₹) at the end of the year 2020-21?
Answer: D. 143.34 — ConceptFor a sequence of yearly values, the annual percentage increase from one year to the next is (new value − old value) ÷ old value × 100. The average…
- A.
135.68
- B.
138.35
- C.
140.17
- D.
143.34
Show answer & explanation
Correct answer: D
Concept
For a sequence of yearly values, the annual percentage increase from one year to the next is (new value − old value) ÷ old value × 100.
The average annual rate is the arithmetic mean of all year-to-year percentage increases. To project the next year, multiply the latest value by 1 + (average rate ÷ 100).
Application
From 2015-16 to 2016-17: (105 − 95) ÷ 95 × 100 = 10.53%.
From 2016-17 to 2017-18: (115 − 105) ÷ 105 × 100 = 9.52%.
From 2017-18 to 2018-19: (126 − 115) ÷ 115 × 100 = 9.57%.
From 2018-19 to 2019-20: (132 − 126) ÷ 126 × 100 = 4.76%.
Using the unrounded yearly rates, average annual rate = [(10 ÷ 95) + (10 ÷ 105) + (11 ÷ 115) + (6 ÷ 126)] ÷ 4 × 100 = 8.5943% (approximately).
Projected 2020-21 value = 132 × (1 + 8.5943 ÷ 100) = 143.3445, which rounds to 143.34 thousand rupees.
Cross-check
Using unrounded yearly rates gives an average of about 8.5943%, and 132 × 1.085943 = 143.3445, which rounds to 143.34.
Therefore, the projected per capita Net National Income is 143.34 thousand rupees.