If 300 families from the "Houseless" category shift into Kutcha houses, what will be the average number of families in every Kutcha house?

Question

Question

Study the following Pie Charts:

This question was previously asked in

UPSC CDS-I 2025 (Elementary Mathematics) Official Paper (Held On: 13 Apr, 2025)

Answer 1

Given:

From Chart-III: Total number of families = 3,60,000

Angle for families in "Houseless" category = 20°

Angle for families "Living in Kutcha houses" = 185°

Number of families from "Houseless" category shifting to Kutcha houses = 300

Formula used:

Number of families for a category = (Angle for category / 360°) × Total number of families

Average families per house = Total families in houses / Total number of houses of that type

Calculations:

Initial Families in Kutcha Houses = (185 / 360) × 3,60,000

⇒ Initial Families in Kutcha Houses = 185 × (3,60,000 / 360) = 1,85,000

Initial Houseless Families = (20 / 360) × 3,60,000

⇒ Initial Houseless Families = 20 × (3,60,000 / 360) = 20,000

New Families in Kutcha Houses = Initial Families in Kutcha Houses + 300

⇒ New Families in Kutcha Houses = 1,85,000 + 300 = 1,85,300

From previous calculations or Chart-I:

Number of Kutcha Houses = (40 / 360) × 1,20,000

⇒ Number of Kutcha Houses = 120000 / 9

Average families per Kutcha house = New Families in Kutcha Houses / Number of Kutcha Houses

⇒ Average families per Kutcha house = 1,85,300 / (120000 / 9)

⇒ Average families per Kutcha house = (1,85,300 × 9) / 120000

⇒ Average families per Kutcha house = 1667700 / 120000

⇒ Average families per Kutcha house = 16677 / 1200

⇒ Average families per Kutcha house ≈ 13.8975 ≈ 13.9

∴ The average number of families in every Kutcha house will be 13.90.