UPSC CDS I 2025 Mathematics Paper

Concept:The number of families in a pie chart category is proportional to its angle. Average families per house is total families divided by number of houses.Explanation:From Chart-III, total families = 3,60,000.Angle for Kutcha houses = 185°, so initial families = $\frac{185}{360} \times 3,60,000 = 1,85,000$.Angle for Houseless = 20°, so initial houseless families = $\frac{20}{360} \times 3,60,000 = 20,000$.After 300 shift, new families in Kutcha houses = $1,85,000 + 300 = 1,85,300$.From Chart-I, total houses = 1,20,000. Angle for Kutcha houses = 40°, so number of Kutcha houses = $\frac{40}{360} \times 1,20,000 = \frac{1,20,000}{9}$.Average families per Kutcha house = $\frac{1,85,300}{\frac{1,20,000}{9}} = \frac{1,85,300 \times 9}{1,20,000} = \frac{16,67,700}{1,20,000} = 13.8975 \approx 13.9$.Answer:B. 13.9