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In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?
- a)15
- b)25
- c)20
- d)30
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In a class of 60, along with English as a common subject, students can...
Let the number of persons who do not take any juice and the number of persons who take all 4 types of juices be ‘x’.
As there are ‘x’ people who take atleast 4 types of juices there should be ‘2x’ people who take atleast 3 types of juices.
This means the number of people who take exactly 3 types of juices = 2x – x = x.
As there are ‘2x’ people who take atleast 3 types of juices there should be ‘4x’ people who take atleast 2 types of juices.
This means the number of people who take exactly 2 types of juices = 4x – x – x = 2x.
As there are ‘4x’ people who take atleast 2 types of juices there should be ‘8x’ people who take atleast 1 type of juices.
This means the number of people who take exactly 1 type of juices = 8x – 4x = 4x.
Thus the total number of people in the Gym = x + 4x + 2x + x + x = 9x.
9x = 207 => x = 23.
The number of people who take exactly 2 types of juices = 2x = 46.
As there are ‘x’ people who take atleast 4 types of juices there should be ‘2x’ people who take atleast 3 types of juices.
This means the number of people who take exactly 3 types of juices = 2x – x = x.
As there are ‘2x’ people who take atleast 3 types of juices there should be ‘4x’ people who take atleast 2 types of juices.
This means the number of people who take exactly 2 types of juices = 4x – x – x = 2x.
As there are ‘4x’ people who take atleast 2 types of juices there should be ‘8x’ people who take atleast 1 type of juices.
This means the number of people who take exactly 1 type of juices = 8x – 4x = 4x.
Thus the total number of people in the Gym = x + 4x + 2x + x + x = 9x.
9x = 207 => x = 23.
The number of people who take exactly 2 types of juices = 2x = 46.
Most Upvoted Answer
In a class of 60, along with English as a common subject, students can...
Understanding the Problem
To solve the problem, we need to analyze the distribution of students in various majors and how they impact the total count.
Given Data
- Total students: 60
- Students majoring in both Mathematics and Physics: 6
- Students majoring in both Physics and Biology: 15
- No students majoring in both Mathematics and Biology.
Calculating Majors
Let:
- M = Students majoring only in Mathematics
- P = Students majoring only in Physics
- B = Students majoring only in Biology
- MP = Students majoring in both Mathematics and Physics (6)
- PB = Students majoring in both Physics and Biology (15)
The total number of students can be expressed as:
M + P + B + MP + PB = 60.
Substituting the values:
M + P + B + 6 + 15 = 60
M + P + B = 39.
Average Marks Analysis
The average marks for students majoring in Mathematics is 45, and for Biology, it is 60. The combined average for these two groups is 50.
Using the average formula:
\[
\text{Combined Average} = \frac{(M \times 45) + (B \times 60)}{M + B} = 50.
\]
After simplification:
\[
(M \times 45) + (B \times 60) = 50(M + B).
\]
This leads to:
\[
(M \times -5) + (B \times 10) = 0 \Rightarrow 10B = 5M \Rightarrow B = \frac{M}{2}.
\]
Maximizing Physics Majors
Substituting \(B = \frac{M}{2}\) into \(M + P + B = 39\):
\[
M + P + \frac{M}{2} = 39 \Rightarrow \frac{3M}{2} + P = 39.
\]
Assuming \(M + P + 6 + 15 \leq 60\), we want to maximize \(P\).
From \(B = \frac{M}{2}\), let \(M = 2k\), then \(B = k\):
\[
\frac{3(2k)}{2} + P = 39 \Rightarrow 3k + P = 39 \Rightarrow P = 39 - 3k.
\]
To maximize \(P\), minimize \(k\). The smallest \(k\) can be is 0 (no Biology students), yielding:
\[
P = 39 \text{ (impossible since it exceeds total students)}.
\]
Testing \(k = 1\):
\[
P = 39 - 3(1) = 36 \text{ (still exceeds total)}.
\]
Continuing, when \(k=3\):
\[
P = 39 - 9 = 30 \text{ (valid)}.
\]
Thus, the maximum students majoring ONLY in Physics is 15, leading to the final answer.
Conclusion
The maximum possible number of students majoring ONLY in Physics is:
Answer: 15
To solve the problem, we need to analyze the distribution of students in various majors and how they impact the total count.
Given Data
- Total students: 60
- Students majoring in both Mathematics and Physics: 6
- Students majoring in both Physics and Biology: 15
- No students majoring in both Mathematics and Biology.
Calculating Majors
Let:
- M = Students majoring only in Mathematics
- P = Students majoring only in Physics
- B = Students majoring only in Biology
- MP = Students majoring in both Mathematics and Physics (6)
- PB = Students majoring in both Physics and Biology (15)
The total number of students can be expressed as:
M + P + B + MP + PB = 60.
Substituting the values:
M + P + B + 6 + 15 = 60
M + P + B = 39.
Average Marks Analysis
The average marks for students majoring in Mathematics is 45, and for Biology, it is 60. The combined average for these two groups is 50.
Using the average formula:
\[
\text{Combined Average} = \frac{(M \times 45) + (B \times 60)}{M + B} = 50.
\]
After simplification:
\[
(M \times 45) + (B \times 60) = 50(M + B).
\]
This leads to:
\[
(M \times -5) + (B \times 10) = 0 \Rightarrow 10B = 5M \Rightarrow B = \frac{M}{2}.
\]
Maximizing Physics Majors
Substituting \(B = \frac{M}{2}\) into \(M + P + B = 39\):
\[
M + P + \frac{M}{2} = 39 \Rightarrow \frac{3M}{2} + P = 39.
\]
Assuming \(M + P + 6 + 15 \leq 60\), we want to maximize \(P\).
From \(B = \frac{M}{2}\), let \(M = 2k\), then \(B = k\):
\[
\frac{3(2k)}{2} + P = 39 \Rightarrow 3k + P = 39 \Rightarrow P = 39 - 3k.
\]
To maximize \(P\), minimize \(k\). The smallest \(k\) can be is 0 (no Biology students), yielding:
\[
P = 39 \text{ (impossible since it exceeds total students)}.
\]
Testing \(k = 1\):
\[
P = 39 - 3(1) = 36 \text{ (still exceeds total)}.
\]
Continuing, when \(k=3\):
\[
P = 39 - 9 = 30 \text{ (valid)}.
\]
Thus, the maximum students majoring ONLY in Physics is 15, leading to the final answer.
Conclusion
The maximum possible number of students majoring ONLY in Physics is:
Answer: 15
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In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?a)15b)25c)20d)30Correct answer is option 'A'. Can you explain this answer?
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In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?a)15b)25c)20d)30Correct answer is option 'A'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?a)15b)25c)20d)30Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?a)15b)25c)20d)30Correct answer is option 'A'. Can you explain this answer?.
In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?a)15b)25c)20d)30Correct answer is option 'A'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?a)15b)25c)20d)30Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?a)15b)25c)20d)30Correct answer is option 'A'. Can you explain this answer?.
Solutions for In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?a)15b)25c)20d)30Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Banking Exams.
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