Classes A and B have 35 students each. If seven girls shift from class A to class B, then the number of girls in the classes would interchange. If four girls shift from class B to class A , then the number of girls in class A would be twice the original number of girls in class B. What is the number of boys in Class A and in Class B?

# Classes A and B have 35 students each. If seven girls shift from class A to class B, then the number of girls in the classes would interchange. If four girls shift from class B to class A , then the number of girls in class A would be twice the original number of girls in class B. What is the number of boys in Class A and in Class B?

1. A
18 and 11
2. B
24 and 17
3. C
18 and 27
4. D
17 and 24

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### Solution:

Let the number of girls in class A=x
Let the number of girls in class B=y
Total students in class A and class B each=35
7 girls shift from class A to class B
Girls in class A= x – 7
Girls in class B= y + 7
After shifting the number of girls in the class interchanged.
x – 7 = y      --------------- (1)
Now, 4 girls are shifted from class B to class A.
Girls in class A= x + 4
Girls in class B= y – 4
So, after shifting
x + 4 = 2y     -------------- (2)
Solving eq (1) and eq (2), we get
x + 4 = 2(x - 7)
x + 4 = 2x – 14
On solving, we get x= 18
Put the value of x in eq (1), we get
18 – 7 =y
y = 11
So, the number of boys in class A= 35 – 18 = 17
The number of boys in class B= 35 – 11 = 24.
Hence, Option (4) is the correct answer.

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