Data Interpretation

To solve the problem, follow these steps:

1. Determine the number of boys and girls in the class based on the given ratio: The ratio of boys to girls is 3:2. Let the number of boys be 3x and the number of girls be 2x. Since the total number of students is 40:
   3x + 2x = 40
   5x = 40
   x = 8
2. Calculate the number of boys and girls:
   Number of boys = 3x = 3(8) = 24
   Number of girls = 2x = 2(8) = 16
3. Calculate the total marks for boys and girls: The average marks for boys is 42, so the total marks for boys: 42 * 24 = 1008. The average marks for girls is 46, so the total marks for girls: 46 * 16 = 736.
4. Determine the average marks for the whole class: The total marks for the entire class is the sum of the total marks for boys and girls:
   Total marks for class = 1008 + 736 = 1744
   Average marks for the whole class = Total marks for class / Total number of students = 1744 / 40 = 43.6

Therefore, the average marks scored by the whole class is 43.6.

To solve the problem, we need to calculate the angle in a pie chart that corresponds to the percentage of students in the Commerce faculty.

1. Understanding the Concepts:

- Pie Chart: A circular chart divided into sectors, each representing a proportion of the whole.
- Total Angle in Circle: A full circle is 360°.
- Angle for a Sector: Calculated using the formula:

2. Given Values:

- Arts: 20%
- Science: 25%
- Law: 15%
- Engineering: 30%
- Commerce = Remaining % = 100% - (20% + 25% + 15% + 30%) = 10%

3. Calculating the Angle for Commerce:

Final Answer:

The angle representing the Commerce faculty in the pie chart is 36 degrees.

To solve the problem, we need to apply the rule of the sequence repeatedly starting from the first term to find the fourth term.

1. Understanding the Concepts:

- Sequence Rule: Each term is generated by multiplying the previous term by 2 and then subtracting 1.
- Recursive Formula: , where
- Goal: Find the value of the 4th term

2. Given Values:

First term
Recursive rule:

3. Calculating the Terms:

Final Answer:

The fourth term in the sequence is 17.

To solve the problem, we need to calculate the simple interest earned over a period based on the principal amount, rate of interest, and time.

1. Understanding the Concepts:

- Principal (P): The initial amount invested.
- Rate of Interest (R): The annual rate at which interest is earned.
- Time (T): The duration for which the money is invested (in years).
- Simple Interest (SI): The interest earned over the period, calculated as:

2. Given Values:

3. Calculating the Simple Interest:

Final Answer:

The total interest earned by the person at the end of the period is Rs 1200.

To solve the problem, we need to find the volume of a cylindrical water tank given its radius and height.

1. Understanding the Formula for Volume of a Cylinder:
The volume of a cylinder is given by the formula:

where is the radius and is the height of the cylinder.

2. Substituting the Given Values:
Given:
Radius
Height

Substitute these into the formula:

3. Simplifying the Expression:
First, calculate :

Now multiply:

Cancel 7 in the denominator with 49:

Final Answer:
The volume of water in the tank is .

To solve the problem, we need to determine the fourth term in a sequence where each term is obtained by multiplying the previous term by 2 and then subtracting 1, starting from the first term which is 3.

1. Understanding the Situation:
- First term (T₁) = 3
- Recursive relation: Tₙ = 2 × Tₙ₋₁ − 1
- We are required to find the fourth term (T₄) of the sequence.

Key Concept: We apply the given recurrence relation repeatedly to compute the next terms based on the previous ones.

2. Generating the Terms:
- T₁ = 3 (given)
- T₂ = 2 × T₁ − 1 = 2 × 3 − 1 = 6 − 1 = 5
- T₃ = 2 × T₂ − 1 = 2 × 5 − 1 = 10 − 1 = 9
- T₄ = 2 × T₃ − 1 = 2 × 9 − 1 = 18 − 1 = 17

Final Answer:
The fourth term in the sequence is 17.

To solve the problem, we need to calculate the total simple interest earned by the person after 3 years.

1. Understanding the Concept of Simple Interest: Simple Interest is the extra money earned or paid for using someone’s money for a certain period of time. It is calculated only on the original principal amount throughout the entire period.

Formula used:

Simple Interest (SI) = (Principal × Rate × Time) / 100

Where: - Principal is the initial amount invested = ₹5000 - Rate is the annual rate of interest = 8% - Time is the duration of investment = 3 years

2. Substituting the Values: We substitute the given values into the formula:

3. Step-by-Step Calculation: First, multiply the numbers in the numerator: Now divide by 100:

4. Interpreting the Result: This means the person earns ₹1200 as interest for keeping ₹5000 invested at 8% for 3 years.

Final Answer: The total interest earned by the person at the end of the period is ₹1200.

To solve the problem, we need to calculate the volume of a completely filled cylindrical water tank using the formula for the volume of a cylinder.

1. Formula for Volume of a Cylinder:
The volume of a cylinder is given by:


where:
- is the radius of the base
- is the height of the cylinder
- (as provided)

2. Substituting the Values:
Given:
-
-

Now substitute into the formula:

3. Simplifying the Expression:

Final Answer:
The volume of water in the tank is 1540 cubic meters.

To solve the problem, we need to determine the total number of students in the remaining four departments, given the average and the number in one department.

1. Understanding the Concepts:

- Average: The sum of values divided by the number of values.
- Total Students: Multiply the average by the number of departments to get the total.
- Subtract: Subtract the number of students in the Science department to find the total in the other departments.

2. Given Values:

- Average number of students = 240
- Number of departments = 5
- Students in Science = 320

3. Calculating Total and Remaining:

Total students in all departments =
Students in other four departments =

Final Answer:

The number of students in the other four departments is 880.