Question

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?
A.18 and 11
B.24 and 17
C.18 and 27
D.17 and 24

Answer 1

Hint: Here, we are required to find the number of boys in Classes A and B respectively. We will assume the number of girls in Classes A and B to be \[x\] and \[y\] respectively. We will then use the given condition and form two equations and solve it to find the number of girls in both the classes. Then we will subtract the number of girls from the total students to get the number of boys in both the classes A and B.

Complete step-by-step answer:
Let the number of girls in Class A be \[ x\] and the number of girls in Class B be \[ y\].
Now, it is given that seven girls shift from class A to class B.
Hence, after shifting,
Number of girls in Class A \[ = x - 7\]
And, number of girls in class B \[ = y + 7\]
Now, it is also given that, if seven girls shift from class A to class B, then the number of girls in the classes would interchange.
Hence, for Class A, number of girls after shifting will be equal to the number of girls in Class B before shifting.
\[x - 7 = y\]
Similarly, for Class B, number of girls after shifting will be equal to the number of girls in Class A before shifting.
This gives us the equation:
\[x = y + 7\]…………………………..\[\left( 1 \right)\]
We know four girls shift from class B to class A.
Hence, after shifting,
Number of girls in Class A \[ = x + 4\]
And, number of girls in class B \[ = y - 4\]
Now, it is given that,
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.
\[x + 4 = 2y\]…………………………..\[\left( 2 \right)\]
Now, substituting the value of \[x\] from equation \[\left( 1 \right)\] in equation \[\left( 2 \right)\], we get
\[y + 7 + 4 = 2y\]
Adding and subtracting the like terms, we get
\[ \Rightarrow y = 11\]
Substituting \[y = 11\] in the equation \[\left( 1 \right)\], we get
\[x = y + 7\]
\[ \Rightarrow x = 11 + 7 = 18\]
Hence, the number of girls in Class A \[ = x = 18\]
Also, it is given that the total number of students in Class A is 35.
Therefore, number of boys in Class A \[ = 35 - 18 = 17\]
Similarly, the number of girls in in Class B \[ = y = 11\]
Also, it is given that the total number of students in Class B is 35.
Therefore, number of boys in Class B \[ = 35 - 11 = 24\]
Hence, the number of boys in Class A and Class B are 17 and 24 respectively.
Therefore, option D is the correct answer.

Note: We might make a mistake by marking option A as answer just by finding the values 18 and 11 as the number of girls. But this will be wrong because in this question, it was asked to find the number of boys and not the number of girls. Hence, it is really important to read the question carefully before marking our answer.