Question 1

In a small college, students are allowed to take only one specialization. Traditionally, only two specializations are offered: Science and Arts. Students enrolled to specialize in Science must take Physics and Mathematics subjects, while students enrolled to specialize in Arts must take Economics and Political Science subjects. Students enrolled in Science are not allowed to take either Economics or Political Science, while students enrolled in Arts are not allowed to take either Physics or Mathematics.

Recently, the college has started a third specialization called MatEco that requires students to take Economics and Mathematics. However, MatEco students would not be allowed to take either Physics or Political Science. When the college opens this new specialization for enrolment, it allows students, originally enrolled in Science or Arts, to switch to MatEco.

From among the students originally enrolled in Arts, 20 students switch to MatEco. This makes the number of Science students twice the number of Arts students. After this, from among the students who originally enrolled in Science, 45 students switch to MatEco. This makes the number of Arts students twice the number of Science students.

In total, how many students, from among those originally enrolled in Science or Arts, are now taking Economics?

Solution

Let's assume that the number of students who initially took Arts is x and the number of students who initially took Science is y.

After 20 students shifted from Arts to MatEco, the number of Science students was twice that of Arts students.

That is y=2*(x-20) => 2x-y-40=0-->1

Now, 45 of the students who originally enrolled in Science have switched to MatEco. This makes the number of Arts students twice the number of Science students.

So, x-20=2*(y-45) => x-2y+70=0-->2

Now that we have two linear equations. Let's solve them.

Multiply Equation 1 with -2 and add it to Equation 2.

-4x+2y+80=0

x-2y+70=0

-3x+150=0

3x=150=>x=50

So, the original number of students enrolled in Arts is 50.

Substitute the value of x in equation 1 to get the y value.

y=60

There are 65 (20 from arts, 45 from Science who shifted to the MatEco) in MatEco. All these study Economics; apart from them, the people currently in Arts also study Economics. There are 50-20=30 people currently in Arts. So, the total number of people who study Economics is 65+30=95.

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