Question

Number of candidates (in thousands) appearing in an examination from four different cities and ratio of passing and failing the given examination is provided in the below table.

The highest number of students pass in the city :

• A. B
• B. A
• C. D
• D. C

Hint:

Always do a quick visual check of the total values.
City B has by far the largest overall candidate base (3.14 thousand) and a passing fraction of over half (5/8 = 62.5%).
This makes it the obvious choice even with a rough approximation, saving you calculation time!

Answer 1

The Correct Option is A

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Step 1: Understanding the Question: This question belongs to the topic of Data Interpretation, involving ratios and percentages.
We need to calculate the actual number of candidates who passed from each of the four given cities (A, B, C, and D) and identify which city has the highest number of passing candidates.

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Step 2: Key Formula or Approach:
If the total number of candidates in a city is \(T\) and the ratio of passing to failing candidates is \(P : F\), then:
\[ \text{Number of passing candidates} = T \times \frac{P}{P + F} \]
We will perform this computation for each of the four cities.

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Step 3: Detailed Explanation:
Let us calculate the passing candidates (in thousands) for each city:
1. City A:
Total candidates = 1.25 thousand
Ratio of Passing : Failing = 7 : 3
Passing candidates:
\[ 1.25 \times \frac{7}{7 + 3} = 1.25 \times \frac{7}{10} = 1.25 \times 0.7 = 0.875 \text{ thousand} \]
So, 875 students passed in City A.
2. City B:
Total candidates = 3.14 thousand
Ratio of Passing : Failing = 5 : 3
Passing candidates:
\[ 3.14 \times \frac{5}{5 + 3} = 3.14 \times \frac{5}{8} = 3.14 \times 0.625 = 1.9625 \text{ thousand} \]
So, 1962.5 students passed in City B.
3. City C:
Total candidates = 1.08 thousand
Ratio of Passing : Failing = 4 : 5
Passing candidates:
\[ 1.08 \times \frac{4}{4 + 5} = 1.08 \times \frac{4}{9} = 1.08 \times 0.4444 = 0.48 \text{ thousand} \]
So, 480 students passed in City C.
4. City D:
Total candidates = 2.27 thousand
Ratio of Passing : Failing = 1 : 3
Passing candidates:
\[ 2.27 \times \frac{1}{1 + 3} = 2.27 \times \frac{1}{4} = 2.27 \times 0.25 = 0.5675 \text{ thousand} \]
So, 567.5 students passed in City D.
Comparing the results:
- City A: 0.875 thousand
- City B: 1.9625 thousand
- City C: 0.48 thousand
- City D: 0.5675 thousand
The highest value is 1.9625 thousand, which occurs in City B.

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Step 4: Final Answer: City B has the highest number of students passing. This corresponds to option (A).