Question

The subject in which he scored \(16\frac{2}{3}\%\) of marks is

• A. Science
• B. Social
• C. Mathematics
• D. Hindi
• A. Science
• B. Social
• C. Mathematics
• D. English
• A. Science
• B. Social
• C. 1st Language
• D. English
• A. 2
• B. 3
• C. 4
• D. 6
• A. Science
• B. Social
• C. 1st Language
• D. Hindi

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Raju's total marks are 554, and the pie chart splits this total across six subjects using degree measures out of a full circle of 360 degrees. We need to find which subject accounts for \(16\frac{2}{3}\%\) of his total marks.

Step 2: Key Formula or Approach:
Since a pie chart represents parts as degrees out of 360, the percentage share of any subject equals its degree value divided by 360, multiplied by 100.
\[ \text{percentage} = \frac{\text{degree}}{360} \times 100 \]
We will find this percentage for each of the four subjects listed in the options and match it against \(16\frac{2}{3}\%\).

Step 3: Detailed Explanation:
Science is marked at 75 degrees, so its share is \(\frac{75}{360} \times 100 = 20.83\%\).
Social is marked at 80 degrees, so its share is \(\frac{80}{360} \times 100 = 22.22\%\).
Mathematics is marked at 72 degrees, so its share is \(\frac{72}{360} \times 100 = 20\%\).
Hindi is marked at 60 degrees, so its share is \(\frac{60}{360} \times 100 = 16.67\%\), the same value as \(16\frac{2}{3}\%\) written as a fraction.
Science, Social, and Mathematics all sit far from \(16\frac{2}{3}\%\), so each of those can be ruled out.

Step 4: Final Answer:
Hindi is the subject in which Raju scored \(16\frac{2}{3}\%\) of the total marks.
\[ \boxed{\text{Hindi}} \]

Answer 2

Step 1: Understanding the Question:
We need to find which subject carries close to 97 marks out of Raju's total of 554, using the degree value shown for each subject in the pie chart.

Step 2: Key Formula or Approach:
Convert each subject's degree value into marks using the relation marks = (degree/360) x 554, since the full circle of 360 degrees stands for the total marks.
\[ \text{marks} = \frac{\text{degree}}{360} \times 554 \]

Step 3: Detailed Explanation:
Science is at 75 degrees: \(\frac{75}{360} \times 554 = 115.42\) marks.
Social is at 80 degrees: \(\frac{80}{360} \times 554 = 123.11\) marks.
Mathematics is at 72 degrees: \(\frac{72}{360} \times 554 = 110.8\) marks.
English is at 63 degrees: \(\frac{63}{360} \times 554 = 96.95\) marks, which rounds to about 97 marks.
Science, Social, and Mathematics all give values well away from 97, so they can be ruled out.

Step 4: Final Answer:
English is the subject in which Raju scored approximately 97 marks.
\[ \boxed{\text{English}} \]

Answer 3

Step 1: Understanding the Question:
We need to find which subject gives Raju the highest percentage of marks out of his total of 554. Since every subject's marks come from the same total, the subject with the largest degree value in the pie chart automatically has the highest percentage.

Step 2: Key Formula or Approach:
The percentage for any subject is proportional to its degree value, so we only need to compare degree values directly instead of converting each one to marks first.
\[ \text{percentage} \propto \text{degree} \]

Step 3: Detailed Explanation:
Science is marked at 75 degrees.
Social is marked at 80 degrees.
1st Language is marked at 90 degrees.
English is marked at 63 degrees.
Comparing these four values, 90 degrees is the largest, so 1st Language has the highest share. As a check, \(\frac{90}{360} \times 100 = 25\%\), which is higher than Social's 22.22%, Science's 20.83%, and English's 17.5%.

Step 4: Final Answer:
1st Language is the subject in which Raju's scoring percentage is the highest.
\[ \boxed{\text{1st Language}} \]

Answer 4

Step 1: Understanding the Question:
We need to split the six subjects into two groups of three: Group A with 1st Language, Hindi and Mathematics, and Group B with Science, Social and English. Then we find the difference between the total marks of Group A and Group B.

Step 2: Key Formula or Approach:
Convert each subject's degree value into marks using marks = (degree/360) x 554, add up each group's marks, and subtract.
\[ \text{marks} = \frac{\text{degree}}{360} \times 554 \]

Step 3: Detailed Explanation:
Group A: 1st Language (90 degrees) = 138.5 marks, Hindi (60 degrees) = 92.33 marks, Mathematics (72 degrees) = 110.8 marks. Adding these, Group A's total is \(138.5 + 92.33 + 110.8 = 341.63\) marks.
Group B: Science (75 degrees) = 115.42 marks, Social (80 degrees) = 123.11 marks, English (63 degrees) = 96.95 marks. Adding these, Group B's total is \(115.42 + 123.11 + 96.95 = 335.48\) marks.
The difference between the two groups is \(341.63 - 335.48 = 6.15\) marks, which rounds to 6 marks.

Step 4: Final Answer:
The difference between the two groups of marks is about 6.
\[ \boxed{6} \]

Answer 5

Step 1: Understanding the Question:
We need to find which subject gives Raju the lowest percentage of marks out of his total of 554. As with the highest percentage question, the percentage is proportional to the degree value, so the subject with the smallest degree has the lowest percentage.

Step 2: Key Formula or Approach:
Compare the degree values of the four subjects in the options directly, since a smaller degree always means a smaller share of the 554 marks.
\[ \text{percentage} \propto \text{degree} \]

Step 3: Detailed Explanation:
Science is marked at 75 degrees.
Social is marked at 80 degrees.
1st Language is marked at 90 degrees.
Hindi is marked at 60 degrees.
Comparing these four values, 60 degrees is the smallest, so Hindi has the lowest share. As a check, \(\frac{60}{360} \times 100 = 16.67\%\), which is lower than Science's 20.83%, Social's 22.22%, and 1st Language's 25%.

Step 4: Final Answer:
Hindi is the subject in which Raju's scoring percentage is the lowest.
\[ \boxed{\text{Hindi}} \]