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There are a total 43800 students in 4 scholl of a city. half the number of first school 2/3 of the second 3/4 of the third and 4/5 of the fourth are all equal. what is the ratio of the number of students of a to d. if a,b,c,d be the first ,second,third, and four schools respectively.?
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There are a total 43800 students in 4 scholl of a city. half the numbe...
Total Students in Four Schools
There are 43,800 students distributed among four schools, denoted as A, B, C, and D.
Equations Based on Given Conditions
We know from the problem statement:
- Half of the number of students in School A: \( \frac{A}{2} \)
- Two-thirds of the number of students in School B: \( \frac{2B}{3} \)
- Three-fourths of the number of students in School C: \( \frac{3C}{4} \)
- Four-fifths of the number of students in School D: \( \frac{4D}{5} \)
All these expressions are equal, so we can set them equal to a common variable \( x \):
- \( \frac{A}{2} = x \) → \( A = 2x \)
- \( \frac{2B}{3} = x \) → \( B = \frac{3x}{2} \)
- \( \frac{3C}{4} = x \) → \( C = \frac{4x}{3} \)
- \( \frac{4D}{5} = x \) → \( D = \frac{5x}{4} \)
Total Students Equation
Now summing all schools gives:
\[
A + B + C + D = 2x + \frac{3x}{2} + \frac{4x}{3} + \frac{5x}{4} = 43800
\]
To combine these, find a common denominator, which is 12:
- \( A = \frac{24x}{12} \)
- \( B = \frac{18x}{12} \)
- \( C = \frac{16x}{12} \)
- \( D = \frac{15x}{12} \)
Thus, summing yields:
\[
\frac{24x + 18x + 16x + 15x}{12} = 43800
\]
This simplifies to:
\[
\frac{73x}{12} = 43800
\]
Solving for \( x \):
\[
73x = 43800 \times 12 \quad \Rightarrow \quad x = \frac{525600}{73} \approx 7200
\]
Calculating Students in Each School
Now substituting \( x \) back to find each school’s students:
- \( A = 2x = 14400 \)
- \( B = \frac{3x}{2} = 10800 \)
- \( C = \frac{4x}{3} = 9600 \)
- \( D = \frac{5x}{4} = 9000 \)
Final Ratio of Students in School A to D
The ratio of students in School A to School D is:
\[
\text{Ratio} = \frac{A}{D} = \frac{14400}{9000} = \frac{16}{10} = \frac{8}{5}
\]
Thus, the final ratio of students in School A to School D is **8:5**.
There are 43,800 students distributed among four schools, denoted as A, B, C, and D.
Equations Based on Given Conditions
We know from the problem statement:
- Half of the number of students in School A: \( \frac{A}{2} \)
- Two-thirds of the number of students in School B: \( \frac{2B}{3} \)
- Three-fourths of the number of students in School C: \( \frac{3C}{4} \)
- Four-fifths of the number of students in School D: \( \frac{4D}{5} \)
All these expressions are equal, so we can set them equal to a common variable \( x \):
- \( \frac{A}{2} = x \) → \( A = 2x \)
- \( \frac{2B}{3} = x \) → \( B = \frac{3x}{2} \)
- \( \frac{3C}{4} = x \) → \( C = \frac{4x}{3} \)
- \( \frac{4D}{5} = x \) → \( D = \frac{5x}{4} \)
Total Students Equation
Now summing all schools gives:
\[
A + B + C + D = 2x + \frac{3x}{2} + \frac{4x}{3} + \frac{5x}{4} = 43800
\]
To combine these, find a common denominator, which is 12:
- \( A = \frac{24x}{12} \)
- \( B = \frac{18x}{12} \)
- \( C = \frac{16x}{12} \)
- \( D = \frac{15x}{12} \)
Thus, summing yields:
\[
\frac{24x + 18x + 16x + 15x}{12} = 43800
\]
This simplifies to:
\[
\frac{73x}{12} = 43800
\]
Solving for \( x \):
\[
73x = 43800 \times 12 \quad \Rightarrow \quad x = \frac{525600}{73} \approx 7200
\]
Calculating Students in Each School
Now substituting \( x \) back to find each school’s students:
- \( A = 2x = 14400 \)
- \( B = \frac{3x}{2} = 10800 \)
- \( C = \frac{4x}{3} = 9600 \)
- \( D = \frac{5x}{4} = 9000 \)
Final Ratio of Students in School A to D
The ratio of students in School A to School D is:
\[
\text{Ratio} = \frac{A}{D} = \frac{14400}{9000} = \frac{16}{10} = \frac{8}{5}
\]
Thus, the final ratio of students in School A to School D is **8:5**.
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There are a total 43800 students in 4 scholl of a city. half the number of first school 2/3 of the second 3/4 of the third and 4/5 of the fourth are all equal. what is the ratio of the number of students of a to d. if a,b,c,d be the first ,second,third, and four schools respectively.?
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There are a total 43800 students in 4 scholl of a city. half the number of first school 2/3 of the second 3/4 of the third and 4/5 of the fourth are all equal. what is the ratio of the number of students of a to d. if a,b,c,d be the first ,second,third, and four schools respectively.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about There are a total 43800 students in 4 scholl of a city. half the number of first school 2/3 of the second 3/4 of the third and 4/5 of the fourth are all equal. what is the ratio of the number of students of a to d. if a,b,c,d be the first ,second,third, and four schools respectively.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are a total 43800 students in 4 scholl of a city. half the number of first school 2/3 of the second 3/4 of the third and 4/5 of the fourth are all equal. what is the ratio of the number of students of a to d. if a,b,c,d be the first ,second,third, and four schools respectively.?.
There are a total 43800 students in 4 scholl of a city. half the number of first school 2/3 of the second 3/4 of the third and 4/5 of the fourth are all equal. what is the ratio of the number of students of a to d. if a,b,c,d be the first ,second,third, and four schools respectively.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about There are a total 43800 students in 4 scholl of a city. half the number of first school 2/3 of the second 3/4 of the third and 4/5 of the fourth are all equal. what is the ratio of the number of students of a to d. if a,b,c,d be the first ,second,third, and four schools respectively.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are a total 43800 students in 4 scholl of a city. half the number of first school 2/3 of the second 3/4 of the third and 4/5 of the fourth are all equal. what is the ratio of the number of students of a to d. if a,b,c,d be the first ,second,third, and four schools respectively.?.
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