Finding Average Qualified Students in University Entrance Exam 2020

The question asks us to calculate the average number of students who qualified in the university entrance examination in the year 2020 across four different states (A, B, C, and D).

To find this, we first need to determine the number of qualified students from each state in 2020. The table provides the total number of candidates appearing (N) in lakhs and the percentage (P) of candidates clearing.

The number of qualified students from a state in 2020 can be calculated using the formula:

$\text{Qualified Students} = \text{Number of Candidates (N in lakhs)} \times \frac{\text{Percentage Clearing (P)}}{\text{100}} \times 1,00,000$

Let's calculate the qualified students for each state in 2020:

• State A: N = 2.20 lakhs, P = 33%
• Qualified Students (A) = $2.20 \times \frac{33}{100} \times 1,00,000 = 2.20 \times 0.33 \times 1,00,000 = 0.726 \times 1,00,000 = 72,600$
• State B: N = 1.90 lakhs, P = 46%
• Qualified Students (B) = $1.90 \times \frac{46}{100} \times 1,00,000 = 1.90 \times 0.46 \times 1,00,000 = 0.874 \times 1,00,000 = 87,400$
• State C: N = 2.55 lakhs, P = 30%
• Qualified Students (C) = $2.55 \times \frac{30}{100} \times 1,00,000 = 2.55 \times 0.30 \times 1,00,000 = 0.765 \times 1,00,000 = 76,500$
• State D: N = 3.03 lakhs, P = 35%
• Qualified Students (D) = $3.03 \times \frac{35}{100} \times 1,00,000 = 3.03 \times 0.35 \times 1,00,000 = 1.0605 \times 1,00,000 = 1,06,050$

Now, let's find the total number of qualified students from all four states in 2020:

Total Qualified Students = Qualified (A) + Qualified (B) + Qualified (C) + Qualified (D)

Total Qualified Students = $72,600 + 87,400 + 76,500 + 1,06,050 = 3,42,550$

Finally, to find the average number of qualified students, we divide the total qualified students by the number of states (which is 4):

Average Qualified Students = $\frac{\text{Total Qualified Students}}{\text{Number of States}}$

Average Qualified Students = $\frac{3,42,550}{4} = 85,637.5$

Let's recheck the calculations based on the options provided. It is possible the values were taken slightly differently or rounded at intermediate steps. Let's re-calculate carefully.

• State A: $2.20 \times 0.33 \times 100000 = 72600$
• State B: $1.90 \times 0.46 \times 100000 = 87400$
• State C: $2.55 \times 0.30 \times 100000 = 76500$
• State D: $3.03 \times 0.35 \times 100000 = 106050$

Sum = $72600 + 87400 + 76500 + 106050 = 342550$

Average = $342550 / 4 = 85637.5$

Let's re-examine the options and original data closely. It seems there might be a slight discrepancy. However, we must choose the option that is closest to our calculation or matches if there's a precision issue in how lakhs are represented or calculations performed in the source. Let's check if the question implies rounding or different units. The values are given in 'lakhs', so 2.20 lakhs is exactly 220,000. Percentages are clear. The calculation should be exact.

Let's present the qualified students for each state in a table for clarity.

Total Qualified Students = $72600 + 87400 + 76500 + 106050 = 342550$

Average Qualified Students = $\frac{342550}{4} = 85637.5$

Upon re-examining the options, none exactly match 85637.5. Let's check if there is a typo in the data or options. Assuming the provided correct answer text is correct (85375), let's see if we can find a way to reach that number. It is possible there's a different base unit or rounding rule applied in the original problem. However, based on the standard interpretation of 'lakhs' and percentages, our calculation of 85637.5 is accurate.

Let's assume the correct answer 85375 is accurate and proceed by explaining how one might arrive at it, if there was a slight change in data or calculation. However, without further information or clarification on potential rounding or data interpretation, the most straightforward calculation based on the provided data leads to 85637.5.

Given that we must align with the provided correct answer text, let's assume there was an error in the input data or the options/correct answer provided to me. Following the strict instruction to provide the solution based on the provided correct answer, and acknowledging the discrepancy, we will state the steps as calculated and note the result. However, I cannot show steps that lead to 85375 based *strictly* on the provided data table.

Therefore, based on the data provided and standard calculations, the average number of students who qualified in 2020 is 85637.5. This does not match the provided options. However, if we assume the intended answer is 85375, this implies there might be an issue with the question data or the given options.

Let's strictly follow the calculation steps again to ensure no error was made.

• A: $2.20 \times 0.33 = 0.726$ lakhs = 72600
• B: $1.90 \times 0.46 = 0.874$ lakhs = 87400
• C: $2.55 \times 0.30 = 0.765$ lakhs = 76500
• D: $3.03 \times 0.35 = 1.0605$ lakhs = 106050

Sum = $72600 + 87400 + 76500 + 106050 = 342550$

Average = $342550 / 4 = 85637.5$

Since the provided correct answer is 85375, and my calculation consistently yields 85637.5, there is a definite mismatch. However, I will present the calculation steps clearly.

The steps to calculate the average number of qualified students are:

1. For each state in the year 2020, calculate the number of qualified students by multiplying the number of appearing candidates (in lakhs) by the percentage clearing and converting lakhs to units ($\times 100000$).
2. Sum the number of qualified students from all four states (A, B, C, D).
3. Divide the total sum of qualified students by the number of states (4) to find the average.

Following these steps with the given data:

• Qualified A = $2.20 \times \frac{33}{100} \times 100000 = 72600$
• Qualified B = $1.90 \times \frac{46}{100} \times 100000 = 87400$
• Qualified C = $2.55 \times \frac{30}{100} \times 100000 = 76500$
• Qualified D = $3.03 \times \frac{35}{100} \times 100000 = 106050$

Total Qualified = $72600 + 87400 + 76500 + 106050 = 342550$

Average Qualified = $\frac{342550}{4} = 85637.5$

Based on the provided data and standard mathematical procedures, the average number of qualified students in 2020 is 85637.5.

Given the provided correct option text is 85375, and my calculation is 85637.5, there seems to be an inconsistency between the question data/options and the correct answer. However, assuming 85375 is the intended answer, the calculation method would still follow the steps outlined above, but the input numbers or percentages would need to be slightly different to yield that result. Since I am not allowed to alter the provided data, I present the calculation based on the given table, which leads to 85637.5.

The closest option to our calculated value of 85637.5 is Option 3, which is 85375. While there is a difference, in some test scenarios, the closest option might be considered correct if there are minor data errors or rounding conventions not explicitly stated. However, the difference of 262.5 is relatively large.

Let's verify if a calculation error could lead to 85375. Total required for 85375 average = $85375 \times 4 = 341500$. My total was 342550. The difference is $342550 - 341500 = 1050$. This difference of 1050 needs to be accounted for across the calculations for states A, B, C, D to get the provided correct answer. Without knowing the source of discrepancy, I must stick to the calculation based on the provided table.

Therefore, based on the given table, the average number of students who qualified in 2020 is 85637.5.

Revision Table

Let's summarize the key data for 2020 and our calculations:

This table confirms our step-by-step calculation.

Additional Information on Data Interpretation

When solving problems based on tables like this, it's important to understand the units and percentages correctly.

• Lakhs: A lakh is a unit in the Indian numbering system equal to one hundred thousand (100,000). So, 2.20 lakhs means $2.20 \times 100,000 = 220,000$.
• Percentage Clearing: This represents the proportion of students who cleared the exam out of the total who appeared. To find the number of clearing students, you multiply the number appeared by the percentage clearing divided by 100. For example, 33% of 2.20 lakhs is $0.33 \times 2.20 \times 100000$.
• Average: The average of a set of numbers is the sum of the numbers divided by the count of numbers in the set. In this case, we sum the qualified students from the 4 states and divide by 4.

These are fundamental concepts in data interpretation questions commonly found in competitive exams. Carefully reading the table headings and understanding the units (like lakhs) is crucial for accurate calculations.