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A school has 1000 students divided into 2 groups, A and B. After a month, 4% of A shifted to B and 25 students from B shifted to A. The number of students in each group stayed the same. How many students did A have?
- a)600
- b)625
- c)500
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A school has 1000 students divided into 2 groups, A and B. After a mo...
To solve this problem, we can use a system of equations to represent the given information. Let's denote the number of students in group A as A and the number of students in group B as B.
1. Setting up the equations:
- Initially, A + B = 1000 (Total number of students in the school)
- After a month, 0.04A students from group A shifted to group B, so the number of students in group A becomes 0.96A.
- Similarly, 25 students from group B shifted to group A, so the number of students in group B becomes B - 25.
2. Equating the number of students in each group:
Since the number of students in each group stayed the same, we can set up the following equation:
0.96A = B - 25
3. Solving the system of equations:
Now, we have two equations:
A + B = 1000 (Equation 1)
0.96A = B - 25 (Equation 2)
We can solve this system of equations by substitution or elimination method. Here, we'll use substitution:
From Equation 1, we have A = 1000 - B
Substituting A in Equation 2, we get:
0.96(1000 - B) = B - 25
960 - 0.96B = B - 25
960 + 25 = B + 0.96B
985 = 1.96B
B = 985/1.96
B ≈ 502
Now, we can substitute the value of B in Equation 1 to find A:
A + 502 = 1000
A = 1000 - 502
A = 498
Therefore, group A initially had 498 students.
However, none of the given options matches this answer. So, there might be an error in the question or the options provided.
1. Setting up the equations:
- Initially, A + B = 1000 (Total number of students in the school)
- After a month, 0.04A students from group A shifted to group B, so the number of students in group A becomes 0.96A.
- Similarly, 25 students from group B shifted to group A, so the number of students in group B becomes B - 25.
2. Equating the number of students in each group:
Since the number of students in each group stayed the same, we can set up the following equation:
0.96A = B - 25
3. Solving the system of equations:
Now, we have two equations:
A + B = 1000 (Equation 1)
0.96A = B - 25 (Equation 2)
We can solve this system of equations by substitution or elimination method. Here, we'll use substitution:
From Equation 1, we have A = 1000 - B
Substituting A in Equation 2, we get:
0.96(1000 - B) = B - 25
960 - 0.96B = B - 25
960 + 25 = B + 0.96B
985 = 1.96B
B = 985/1.96
B ≈ 502
Now, we can substitute the value of B in Equation 1 to find A:
A + 502 = 1000
A = 1000 - 502
A = 498
Therefore, group A initially had 498 students.
However, none of the given options matches this answer. So, there might be an error in the question or the options provided.
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Community Answer
A school has 1000 students divided into 2 groups, A and B. After a mo...
4% of the students of A = 25. So, answer is 625
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A school has 1000 students divided into 2 groups, A and B. After a month, 4% of A shifted to B and 25 students from B shifted to A. The number of students in each group stayed the same. How many students did A have?a)600b)625c)500d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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