Question

Number of students in five sections are represented in below table. Male and Female ratio section wise is also provided in table. Arrange the section according to Female students in ascending order.

Choose the correct answer from the options given below:

• A. C, B, D, A, E
• B. A, D, E, B, C
• C. A, E, D, B, C
• D. C, B, D, E, A

Hint:

To save calculation steps, check extreme cases first.
Section \(\gamma\) has only 5/12 females (less than half of 240, so < 120), making it the lowest.
Section \(\alpha\) has 3/4 females (75% of 280 = 210), making it the highest.
Looking at the options, only option (D) starts with C and ends with A!

Answer 1

The Correct Option is D

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Step 1: Understanding the Question: This question involves processing tabular data by applying ratios to absolute numbers.
We need to calculate the actual number of female students in each of the five given sections (\(\alpha, \beta, \gamma, \theta, \xi\)) and then arrange the sections in ascending order (smallest to largest) of these counts.

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Step 2: Key Formula or Approach:
If the total number of students in a section is \(S\) and the ratio of males to females is \(M : F\), then:
\[ \text{Number of Female Students} = S \times \frac{F}{M + F} \]

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Step 3: Detailed Explanation:
Let us calculate the female students in each section:
1. Section \(\alpha\) (corresponds to A):
Total students = 280
Male : Female = 1 : 3
Female students:
\[ 280 \times \frac{3}{1 + 3} = 280 \times \frac{3}{4} = 70 \times 3 = 210 \]
2. Section \(\beta\) (corresponds to B):
Total students = 290
Male : Female = 3 : 2
Female students:
\[ 290 \times \frac{2}{3 + 2} = 290 \times \frac{2}{5} = 58 \times 2 = 116 \]
3. Section \(\gamma\) (corresponds to C):
Total students = 240
Male : Female = 7 : 5
Female students:
\[ 240 \times \frac{5}{7 + 5} = 240 \times \frac{5}{12} = 20 \times 5 = 100 \]
4. Section \(\theta\) (corresponds to D):
Total students = 270
Male : Female = 4 : 5
Female students:
\[ 270 \times \frac{5}{4 + 5} = 270 \times \frac{5}{9} = 30 \times 5 = 150 \]
5. Section \(\xi\) (corresponds to E):
Total students = 300
Male : Female = 2 : 3
Female students:
\[ 300 \times \frac{3}{2 + 3} = 300 \times \frac{3}{5} = 60 \times 3 = 180 \]
Now, let us list the sections with their respective female counts:
- Section \(\gamma\) (C) = 100
- Section \(\beta\) (B) = 116
- Section \(\theta\) (D) = 150
- Section \(\xi\) (E) = 180
- Section \(\alpha\) (A) = 210
Arranging these counts in ascending order (smallest to largest):
\[ 100 < 116 < 150 < 180 < 210 \]
Which corresponds to the order:
\[ \gamma \rightarrow \beta \rightarrow \theta \rightarrow \xi \rightarrow \alpha \]
In terms of letters: C, B, D, E, A.

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Step 4: Final Answer: The sections arranged in ascending order of female students is C, B, D, E, A, which corresponds to option (D).