There are only two hostels in XYZ University, Hostel P and Hostel Q, wherein an equal number of students were living in year 2021. The total number of persons living in both hostels of XYZ University fell by 33% to 8,375 in 2022 from 2021. How many students were living in Hostel P in 2021?

Correct option is C

Given:

Equal number of people live in both hostels

Number of people living fell by 33% in 2022 from 2021

Number of people left in 2022 = 8375

Solution:

Let the number of people living in 2021 be 100

Then people living in 2022 be 100 - 33% of 100 = 67

But $$67 \equiv 8375$$​​

​$$100 \equiv \frac{8375}{67}\times 100 = 12,500$$​​

Number of people living in hostel P = $$\frac{12,500}{2} = 6,250$$  (Equal number of people in both hostels)​