a university has 4000 students these students are divided into four categories btech,mtech,ms,phd 3100 students joined in B.tech 350 students in mtech and 150 students in ms find the number of students entrooled in phd and find the percentage of the students in eachb category

3100 + 350 + 150 + phd = 4000

Now finish it off

To find the number of students enrolled in PhD, we need to subtract the number of students enrolled in B.Tech, M.Tech, and MS from the total number of students.

Total number of students = 4000
Number of students in B.Tech = 3100
Number of students in M.Tech = 350
Number of students in MS = 150

Number of students in PhD = Total number of students - (Number of students in B.Tech + Number of students in M.Tech + Number of students in MS)
= 4000 - (3100 + 350 + 150)
= 4000 - 3600
= 400

To find the percentage of students in each category, we can use the following formulas:

Percentage of students in B.Tech = (Number of students in B.Tech / Total number of students) * 100
Percentage of students in M.Tech = (Number of students in M.Tech / Total number of students) * 100
Percentage of students in MS = (Number of students in MS / Total number of students) * 100
Percentage of students in PhD = (Number of students in PhD / Total number of students) * 100

Now let's calculate the percentages for each category:

Percentage of students in B.Tech = (3100 / 4000) * 100 = 77.5%
Percentage of students in M.Tech = (350 / 4000) * 100 = 8.75%
Percentage of students in MS = (150 / 4000) * 100 = 3.75%
Percentage of students in PhD = (400 / 4000) * 100 = 10%