Question

What is the total number of marks secured by the student in all the subjects put together?

• A. \(360\)
• B. \(450\)
• C. \(540\)
• D. \(720\)
• A. \(108\)
• B. \(114\)
• C. \(120\)
• D. \(136\)
• A. \(2:3\)
• B. \(3:4\)
• C. \(4:5\)
• D. \(5:6\)
• A. \(15\)
• B. \(20\)
• C. \(25\)
• D. \(30\)
• A. \(45\)
• B. \(35\)
• C. \(25\)
• D. \(30\)
• A. \(249\)
• B. \(183\)
• C. \(225\)
• D. \(222\)
• A. Hindi
• B. English
• C. Maths
• D. Science

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
We need to find the total marks corresponding to the entire pie chart (360��).

Step 2: Key Formula or Approach:
Using the conversion factor derived from the information about Mathematics (1�� = 1.5 marks), we can calculate the total marks. Total Marks = Total Angle \(\times\) Marks per Degree.

Step 3: Detailed Explanation:
The total angle of the pie chart is 360��. The conversion factor is 1.5 marks per degree. \[ \text{Total Marks} = 360^\circ \times 1.5 \frac{\text{marks}}{^\circ} \] \[ \text{Total Marks} = 360 \times \frac{3}{2} = 180 \times 3 = 540 \] So, the total marks secured by the student are 540.

Step 4: Final Answer:
The total number of marks is 540, which corresponds to option (C).

Answer 2

Step 1: Understanding the Concept:
We need to calculate the marks for a specific subject (Science) using its angle in the pie chart and the conversion factor we previously established.

Step 2: Key Formula or Approach:
Marks in Subject = Angle of Subject \(\times\) Marks per Degree. From the pie chart, the angle for Science is 76��. The conversion factor is 1.5 marks per degree.

Step 3: Detailed Explanation:
Angle for Science = 76��. Marks per degree = 1.5. \[ \text{Marks in Science} = 76^\circ \times 1.5 \frac{\text{marks}}{^\circ} \] \[ \text{Marks in Science} = 76 \times \frac{3}{2} = 38 \times 3 = 114 \] The student scored 114 marks in Science.

Step 4: Final Answer:
The marks in Science are 114, which corresponds to option (B).

Answer 3

Step 1: Understanding the Concept:
We need to find the ratio of marks between two subjects. In a pie chart, the ratio of the values represented by two sectors is equal to the ratio of their central angles.

Step 2: Key Formula or Approach:
Ratio of Marks = Ratio of Angles. From the pie chart: - Angle for Hindi = 60�� - Angle for Social Studies = 72��

Step 3: Detailed Explanation:
The ratio of marks scored in Hindi to Social Studies is the same as the ratio of their corresponding angles. \[ \text{Ratio} = \frac{\text{Marks in Hindi}}{\text{Marks in Social Studies}} = \frac{\text{Angle for Hindi}}{\text{Angle for Social Studies}} = \frac{60^\circ}{72^\circ} \] Now, we simplify the fraction \(\frac{60}{72}\). Both numbers are divisible by their greatest common divisor, which is 12. \[ \frac{60 \div 12}{72 \div 12} = \frac{5}{6} \] The ratio is 5:6.
Alternatively, one could calculate the marks: Marks in Hindi = \(60 \times 1.5 = 90\). Marks in Social Studies = \(72 \times 1.5 = 108\). Ratio = \(90:108\). Dividing both by their GCD (18) gives \(5:6\).

Step 4: Final Answer:
The ratio is 5:6, which corresponds to option (D).

Answer 4

Step 1: Understanding the Concept:
We need to express the marks in Social Studies as a percentage of the total marks. This percentage will be the same as the percentage of the total angle that the Social Studies sector represents.

Step 2: Key Formula or Approach:
\[ \text{Percentage} = \frac{\text{Angle for Subject}}{\text{Total Angle}} \times 100\% \] From the pie chart: - Angle for Social Studies = 72�� - Total Angle = 360��

Step 3: Detailed Explanation:
Using the angles to find the percentage: \[ \text{Percentage for Social Studies} = \frac{72^\circ}{360^\circ} \times 100\% \] Simplify the fraction \(\frac{72}{360}\). We know that \(72 \times 5 = 360\), so the fraction is \(\frac{1}{5}\). \[ \text{Percentage} = \frac{1}{5} \times 100\% = 20\% \] Alternatively, using the marks: Total Marks = 540. Marks in Social Studies = Angle \(\times\) 1.5 = \(72 \times 1.5 = 108\). Percentage = \(\frac{108}{540} \times 100\% = \frac{1}{5} \times 100\% = 20\%\).

Step 4: Final Answer:
The percentage of marks in Social Studies is 20%, which corresponds to option (B).

Answer 5

Step 1: Understanding the Concept:
We need to find the absolute difference between the marks obtained in two subjects, Hindi and Maths.

Step 2: Key Formula or Approach:
We can find the difference in two ways: 1. Calculate the marks for each subject separately and then subtract them. 2. Find the difference in their angles first, and then convert that angle difference to marks. Method 2 is generally faster. Difference in Marks = (Difference in Angles) \(\times\) Marks per Degree.

Step 3: Detailed Explanation:
From the problem statement and pie chart: - Marks in Maths = 135 (given) - Angle for Hindi = 60�� - Marks per degree = 1.5 Method 1: Calculate marks separately - Marks in Maths = 135. - Marks in Hindi = Angle for Hindi \(\times\) 1.5 = \(60^\circ \times 1.5 = 90\). - Difference = Marks in Maths - Marks in Hindi = \(135 - 90 = 45\). Method 2: Using angle difference - Angle for Maths = 90�� - Angle for Hindi = 60�� - Difference in Angles = \(90^\circ - 60^\circ = 30^\circ\). - Difference in Marks = \(30^\circ \times 1.5 \frac{\text{marks}}{^\circ} = 45\).

Step 4: Final Answer:
The difference between the marks of Hindi and Maths is 45, which corresponds to option (A).

Answer 6

Step 1: Understanding the Concept:
We need to find the sum of the marks obtained in two subjects, Science and Social Studies, based on the given pie chart.

Step 2: Key Formula or Approach:
We can find the total marks in two ways: 1. Calculate the marks for each subject individually and then add them. 2. Add the angles for the two subjects first, and then convert the total angle to marks. Method 2 is generally quicker. Total Marks = (Total Angle) \(\times\) (Marks per Degree)

Step 3: Detailed Explanation:
From the pie chart: - Angle for Science = 76�� - Angle for Social Studies = 72�� The conversion factor is 1.5 marks per degree. Method 1: Calculate marks separately - Marks in Science = \(76 \times 1.5 = 114\) - Marks in Social Studies = \(72 \times 1.5 = 108\) - Total Marks = \(114 + 108 = 222\) Method 2: Using total angle - Total angle for Science and Social Studies = \(76^\circ + 72^\circ = 148^\circ\) - Total Marks = \(148^\circ \times 1.5 \frac{\text{marks}}{^\circ}\) - Total Marks = \(148 \times \frac{3}{2} = 74 \times 3 = 222\) Both methods give the same result.

Step 4: Final Answer:
The total marks in Science and Social Studies are 222, which corresponds to option (D).

Answer 7

Step 1: Understanding the Concept:
We are given a specific mark value (93) and need to identify the subject it corresponds to. We can do this by converting the given marks into a central angle and then matching that angle with the subjects in the pie chart.

Step 2: Key Formula or Approach:
We use the conversion factor in reverse. Conversion: 1.5 marks = 1�� So, Angle = Marks 1.5 = Marks (3/2) = Marks \(\times \frac{2}{3}\). We will calculate the angle for 93 marks and identify the subject.

Step 3: Detailed Explanation:
We are given the marks = 93. Let's find the corresponding angle: \[ \text{Angle} = 93 \times \frac{2}{3} = 31 \times 2 = 62^\circ \] Now we look at the pie chart to see which subject has a central angle of 62��. From the chart: - Hindi: 60�� - English: 62�� - Maths: 90�� - Science: 76�� - Social Studies: 72�� The angle 62�� corresponds to the subject English.

Step 4: Final Answer:
The student scored 93 marks in English, which corresponds to option (B).