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There are two examination rooms A and B. If 15 candidates are sent from A to B, the number of students in each room is the same. If 25 candidates are sent from B to A, the number of students in A is double of that in B. Find the number of students in each room.
- a)100 in A and 102 in B
- b)135 in A and 105 in B
- c)125 in A and 100 in B
- d)105 in A and 120 in B
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
There are two examination rooms A and B. If 15 candidates are sent fro...
Let the number of students in rooms A and B be x and y respectively.
⇒ x - 15 = y + 15
⇒ x - y = 30 - - - - - equation 1
Also from the given data
⇒ x + 25 = 2 (y - 25)
⇒ x + 25 = 2y - 50
⇒ x - 2y = -75 - - - - - - - equation 2
From equation 1 and equation 2, we get
⇒ Equation 1 - Equation 2, we get y = 105
Substitute y = 105 in equation 1, we get
⇒ x = 135
∴ Number of students in rooms A and B are 135 and 105
Most Upvoted Answer
There are two examination rooms A and B. If 15 candidates are sent fro...
Problem Analysis:
Let's assume the number of students in room A is 'a' and the number of students in room B is 'b'. According to the given conditions:
1. If 15 candidates are sent from A to B, the number of students in each room is the same. This means that after the transfer, both rooms will have the same number of students. Therefore, we can write the equation as:
a - 15 = b + 15 ... (Equation 1)
2. If 25 candidates are sent from B to A, the number of students in A is double that in B. This means that after the transfer, the number of students in A will be double the number of students in B. Therefore, we can write the equation as:
a + 25 = 2(b - 25) ... (Equation 2)
Solving the Equations:
We can solve these two equations to find the values of 'a' and 'b'.
Simplifying Equation 1:
a - 15 = b + 15
a - b = 30 ... (Equation 3)
Simplifying Equation 2:
a + 25 = 2(b - 25)
a + 25 = 2b - 50
a - 2b = -75 ... (Equation 4)
Now, we can solve Equations 3 and 4 simultaneously to find the values of 'a' and 'b'.
Multiplying Equation 3 by 2:
2(a - b) = 2(30)
2a - 2b = 60 ... (Equation 5)
Adding Equation 5 and Equation 4:
(2a - 2b) + (a - 2b) = 60 + (-75)
3a - 4b = -15 ... (Equation 6)
Solving Equation 6 for 'a':
3a - 4b = -15
3a = 4b - 15
a = (4b - 15)/3 ... (Equation 7)
Substituting the Value of 'a' in Equation 7:
Substituting the value of 'a' from Equation 7 into Equation 3:
(4b - 15)/3 - b = 30
4b - 15 - 3b = 90
b - 15 = 90
b = 105
Substituting the value of 'b' in Equation 7 to find 'a':
a = (4(105) - 15)/3
a = 420/3
a = 140
Therefore, the number of students in room A is 140 and the number of students in room B is 105.
Final Answer:
The number of students in each room is 140 in A and 105 in B. Therefore, the correct answer is option 'B'.
Let's assume the number of students in room A is 'a' and the number of students in room B is 'b'. According to the given conditions:
1. If 15 candidates are sent from A to B, the number of students in each room is the same. This means that after the transfer, both rooms will have the same number of students. Therefore, we can write the equation as:
a - 15 = b + 15 ... (Equation 1)
2. If 25 candidates are sent from B to A, the number of students in A is double that in B. This means that after the transfer, the number of students in A will be double the number of students in B. Therefore, we can write the equation as:
a + 25 = 2(b - 25) ... (Equation 2)
Solving the Equations:
We can solve these two equations to find the values of 'a' and 'b'.
Simplifying Equation 1:
a - 15 = b + 15
a - b = 30 ... (Equation 3)
Simplifying Equation 2:
a + 25 = 2(b - 25)
a + 25 = 2b - 50
a - 2b = -75 ... (Equation 4)
Now, we can solve Equations 3 and 4 simultaneously to find the values of 'a' and 'b'.
Multiplying Equation 3 by 2:
2(a - b) = 2(30)
2a - 2b = 60 ... (Equation 5)
Adding Equation 5 and Equation 4:
(2a - 2b) + (a - 2b) = 60 + (-75)
3a - 4b = -15 ... (Equation 6)
Solving Equation 6 for 'a':
3a - 4b = -15
3a = 4b - 15
a = (4b - 15)/3 ... (Equation 7)
Substituting the Value of 'a' in Equation 7:
Substituting the value of 'a' from Equation 7 into Equation 3:
(4b - 15)/3 - b = 30
4b - 15 - 3b = 90
b - 15 = 90
b = 105
Substituting the value of 'b' in Equation 7 to find 'a':
a = (4(105) - 15)/3
a = 420/3
a = 140
Therefore, the number of students in room A is 140 and the number of students in room B is 105.
Final Answer:
The number of students in each room is 140 in A and 105 in B. Therefore, the correct answer is option 'B'.
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There are two examination rooms A and B. If 15 candidates are sent from A to B, the number of students in each room is the same. If 25 candidates are sent from B to A, the number of students in A is double of that in B. Find the number of students in each room.a)100 in A and 102 in Bb)135 in A and 105 in Bc)125 in A and 100 in Bd)105 in A and 120 in BCorrect answer is option 'B'. Can you explain this answer?
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There are two examination rooms A and B. If 15 candidates are sent from A to B, the number of students in each room is the same. If 25 candidates are sent from B to A, the number of students in A is double of that in B. Find the number of students in each room.a)100 in A and 102 in Bb)135 in A and 105 in Bc)125 in A and 100 in Bd)105 in A and 120 in BCorrect answer is option 'B'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about There are two examination rooms A and B. If 15 candidates are sent from A to B, the number of students in each room is the same. If 25 candidates are sent from B to A, the number of students in A is double of that in B. Find the number of students in each room.a)100 in A and 102 in Bb)135 in A and 105 in Bc)125 in A and 100 in Bd)105 in A and 120 in BCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two examination rooms A and B. If 15 candidates are sent from A to B, the number of students in each room is the same. If 25 candidates are sent from B to A, the number of students in A is double of that in B. Find the number of students in each room.a)100 in A and 102 in Bb)135 in A and 105 in Bc)125 in A and 100 in Bd)105 in A and 120 in BCorrect answer is option 'B'. Can you explain this answer?.
There are two examination rooms A and B. If 15 candidates are sent from A to B, the number of students in each room is the same. If 25 candidates are sent from B to A, the number of students in A is double of that in B. Find the number of students in each room.a)100 in A and 102 in Bb)135 in A and 105 in Bc)125 in A and 100 in Bd)105 in A and 120 in BCorrect answer is option 'B'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about There are two examination rooms A and B. If 15 candidates are sent from A to B, the number of students in each room is the same. If 25 candidates are sent from B to A, the number of students in A is double of that in B. Find the number of students in each room.a)100 in A and 102 in Bb)135 in A and 105 in Bc)125 in A and 100 in Bd)105 in A and 120 in BCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two examination rooms A and B. If 15 candidates are sent from A to B, the number of students in each room is the same. If 25 candidates are sent from B to A, the number of students in A is double of that in B. Find the number of students in each room.a)100 in A and 102 in Bb)135 in A and 105 in Bc)125 in A and 100 in Bd)105 in A and 120 in BCorrect answer is option 'B'. Can you explain this answer?.
Solutions for There are two examination rooms A and B. If 15 candidates are sent from A to B, the number of students in each room is the same. If 25 candidates are sent from B to A, the number of students in A is double of that in B. Find the number of students in each room.a)100 in A and 102 in Bb)135 in A and 105 in Bc)125 in A and 100 in Bd)105 in A and 120 in BCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Railways.
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There are two examination rooms A and B. If 15 candidates are sent from A to B, the number of students in each room is the same. If 25 candidates are sent from B to A, the number of students in A is double of that in B. Find the number of students in each room.a)100 in A and 102 in Bb)135 in A and 105 in Bc)125 in A and 100 in Bd)105 in A and 120 in BCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for There are two examination rooms A and B. If 15 candidates are sent from A to B, the number of students in each room is the same. If 25 candidates are sent from B to A, the number of students in A is double of that in B. Find the number of students in each room.a)100 in A and 102 in Bb)135 in A and 105 in Bc)125 in A and 100 in Bd)105 in A and 120 in BCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of There are two examination rooms A and B. If 15 candidates are sent from A to B, the number of students in each room is the same. If 25 candidates are sent from B to A, the number of students in A is double of that in B. Find the number of students in each room.a)100 in A and 102 in Bb)135 in A and 105 in Bc)125 in A and 100 in Bd)105 in A and 120 in BCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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