Question : Directions: In a college, the total number of students who opted for Biology or Chemistry is 150. Later, 12 students who opted for Biology changed their preference and opted for Chemistry. Now, the number of students in Biology is half the number of students in Chemistry. How many students are in Chemistry now?
Option 1: 88
Option 2: 94
Option 3: 104
Option 4: 100
Correct Answer: 100
Solution :
Given:
The total number of students = 150
Let the number of students who opted for biology = x
and the number of students who opted for chemistry = y
This means –
x + y = 150 — (i)
Now, 12 students who opted for Biology changed their preference and opted for Chemistry.
So, the new number of students who opted for biology = x – 12
and the new number of students who opted for chemistry = y + 12
The number of students in Biology is half the number of students in Chemistry –
(x – 12) = (y + 12) ÷ 2
2(x – 12) = y + 12
2x – 24 = y + 12
2x – y = 36 — (ii)
Adding the equations (i) and (ii) –
x + y + 2x – y = 150 + 36
3x = 186
x = 186 ÷ 3
x = 62
Now, put the value of x in the equation (i) –
62 + y = 150
y = 150 – 62 = 88
So, the students who opted for chemistry now are (88 + 12) = 100. Hence, the fourth option is correct.
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