UPSC CDS I 2025 Mathematics Paper

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∘