If 5000 more Kutcha houses are built, then what will be approximate change in angle for Kutcha houses in Pie Chart-I?

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-I: Initial total number of houses = 1,20,000

Initial angle for Kutcha houses = 40°

Increase in Kutcha houses = 5000

Formula used:

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

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

Calculations:

Initial number of Kutcha houses = (40 / 360) × 1,20,000

⇒ Initial number of Kutcha houses = (1 / 9) × 1,20,000

⇒ Initial number of Kutcha houses = 120000 / 9

New total number of houses = Initial total number of houses + 5000

⇒ New total number of houses = 1,20,000 + 5000

⇒ New total number of houses = 1,25,000

New number of Kutcha houses = Initial number of Kutcha houses + 5000

⇒ New number of Kutcha houses = (120000 / 9) + 5000

⇒ New number of Kutcha houses = (120000 + 45000) / 9

⇒ New number of Kutcha houses = 165000 / 9

New angle for Kutcha houses = (New number of Kutcha houses / New total number of houses) × 360°

⇒ New angle for Kutcha houses = ((165000 / 9) / 125000) × 360°

⇒ (165000 / (9 × 125000)) × 360°

⇒ (165 / (9 × 125)) × 360°

⇒ (11 / 75) × 360° = 11 × 4.8 = 52.8°

Change in angle = New angle for Kutcha houses - Initial angle for Kutcha houses

⇒ Change in angle = 52.8° - 40°

⇒ Change in angle = 12.8° ≈ 13°

∴ The approximate change in angle for Kutcha houses in Pie Chart-I will be 12.8°.