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

With reference to the year 2015-16, the percentagem growth in the population of India by the year 2019-20 is

The correct option is ∼ 4.4%.

Step 1: Understand the mathematical relationship
Per Capita Net National Income (PCNNI) is calculated by dividing the Net National Income (NNI) by the total population of the country. We can express this relation as:

$$\text{Per Capita Net National Income}=\frac{\text{Net National Income}}{\text{Population}}$$

By rearranging this formula, we can express the population as:

$$\text{Population}=\frac{\text{Net National Income}}{\text{Per Capita Net National Income}}$$

Step 2: Retrieve the data points from the table
From the table provided, we locate the values of Net National Income and Per Capita Net National Income for the baseline year 2015-16 and the target year 2019-20:
• For the year 2015-16, the Net National Income is 122 Lac Crore rupees, and the Per Capita Net National Income is 95 thousand rupees.
• For the year 2019-20, the Net National Income is 177 Lac Crore rupees, and the Per Capita Net National Income is 132 thousand rupees.

Step 3: Define the population expressions for both years
To keep the units consistent, we note the conversion factors:
1 Lac Crore = 10¹²
1 Thousand = 10³
Therefore, the population of India for the two years can be written as follows:

For the year 2015-16:

$$P_{\text{2015-16}}=\frac{122\times {10}^{12}}{95\times {10}^3}=\frac{122}{95}\times {10}^9$$

For the year 2019-20:

$$P_{\text{2019-20}}=\frac{177\times {10}^{12}}{132\times {10}^3}=\frac{177}{132}\times {10}^9$$

Step 4: Find the ratio of the population in 2019-20 to 2015-16
We compute the ratio of the population in 2019-20 to the population in 2015-16:

$$\frac{P_{\text{2019-20}}}{P_{\text{2015-16}}}=\frac{\frac{177}{132}\times {10}^9}{\frac{122}{95}\times {10}^9}=\frac{177}{132}\times \frac{95}{122}$$

Let us calculate the product of the terms in the numerator and the denominator:

Numerator calculation:

$$177\times 95=16815$$

Denominator calculation:

$$132\times 122=16104$$

Substituting these products back into the ratio:

$$\frac{P_{\text{2019-20}}}{P_{\text{2015-16}}}=\frac{16815}{16104}\approx 1.04415$$

Step 5: Calculate the percentage growth in population
The formula for percentage growth is:

$$\text{Percentage Growth}=\left(\frac{P_{\text{2019-20}}}{P_{\text{2015-16}}}-1\right)\times 100$$

Substituting our calculated ratio:

$$\text{Percentage Growth}=\left(1.04415-1\right)\times 100$$

$$\text{Percentage Growth}=0.04415\times 100=4.415\%\approx 4.4\%$$

Thus, the percentage growth in the population of India by the year 2019-20 with reference to 2015-16 is approximately 4.4%.