Q.A country's national income was ₹500 crore in 2020 with a population of 50 lakh, and rose to ₹650 crore in 2023 with a population of 52 lakh. Calculate the per-capita income for both years and the percentage growth in per-capita income over the period.

Per-capita income must be recomputed for each year separately before comparing, since BOTH national income and population changed over the period.

Formula: $\text{Per-Capita Income} = \dfrac{\text{National Income}}{\text{Population}}$

Method 1 — direct computation:

2020: National income = ₹500 crore = ₹5,00,00,00,000; Population = 50 lakh = 50,00,000.

2023: National income = ₹650 crore = ₹6,50,00,00,000; Population = 52 lakh = 52,00,000.

Growth in PCI $= \dfrac{1{,}250 - 1{,}000}{1{,}000} \times 100 = 25\%$

Method 2 — independent cross-check (crore/lakh ratio shortcut, since 1 crore ÷ 1 lakh = 100):

$PCI_{2020} = \dfrac{500}{50} \times 100 = 10 \times 100 = ₹1{,}000$

$PCI_{2023} = \dfrac{650}{52} \times 100 = 12.5 \times 100 = ₹1{,}250$

Both methods agree exactly, confirming PCI rose from ₹1,000 to ₹1,250 — a 25% increase over the three years.

Convert national income (crore) and population (lakh) to consistent absolute units, divide national income by population separately for each year to get per-capita income, then find the percentage change between the two years; cross-check using the crore-to-lakh ratio shortcut.

Computing the percentage growth of national income (30%) or the percentage growth of population (4%) and mistaking either for the growth in per-capita income — per-capita income growth must account for BOTH changes together, by recomputing the ratio for each year separately, not simply subtracting the two growth rates.