If 45 percent of the students of a class have offered mathematics and 85 percent of them biology, find the percentage of students who offered biology only?
To find the percentage of students who offered biology only, we need to first determine the number of students who offered both mathematics and biology.
Let's assume there are 100 students in the class.
Given that 45% of the students offered mathematics, this means that 45 percent of 100 students equals (45/100)*100 = 45 students offered mathematics.
Also given that 85% of the students offered biology, this means that 85 percent of 100 students equals (85/100)*100 = 85 students offered biology.
However, we're interested in finding the percentage of students who offered biology only. So we need to subtract the number of students who offered both mathematics and biology from the total number of students who offered biology.
Let's assume "x" students offered both mathematics and biology. Therefore, the number of students who offered biology only is 85 - x.
Since both mathematics and biology are subjects offered by the students, the total number of students who offered only mathematics, only biology, or both is equal to the total number of students, which is 100.
So, we can set up the equation:
Number of students who offered only mathematics + Number of students who offered only biology + Number of students who offered both mathematics and biology = Total number of students
45 + (85 - x) + x = 100
45 + 85 - x + x = 100
130 - x = 100
Simplifying the equation, we find:
x = 130 - 100
x = 30
Therefore, 30 students offered both mathematics and biology.
Now, to find the percentage of students who offered biology only, we substitute x = 30 into the equation:
Number of students who offered only biology = 85 - x
Number of students who offered only biology = 85 - 30
Number of students who offered only biology = 55
So, 55 students offered biology only.
Finally, to find the percentage of students who offered biology only, we divide the number of students who offered biology only (55) by the total number of students (100) and multiply by 100:
Percentage of students who offered biology only = (55/100) * 100
Percentage of students who offered biology only = 55%
Therefore, the percentage of students who offered biology only is 55%.
100=45+85-both
both=30
which means biology only is 85-30