https://file.aiquickdraw.com/mathbot/file/17263800335882482hxr2.jpg

Let's go through the problems step by step. I'll solve a few from each section to help you understand the solutions:

### Question 1:
**Marish has some shares of ₹20 of a company paying 12% dividend. If his annual income is ₹960, then the number of shares he bought is:**

Given:
- Dividend = 12%
- Face value of shares = ₹20
- Annual income from shares = ₹960

The formula for the dividend income is:
\[
\text{Dividend Income} = \text{Number of Shares} \times \left(\frac{\text{Dividend Rate}}{100}\right) \times \text{Face Value}
\]

Let the number of shares be \( N \).

\[
960 = N \times \left(\frac{12}{100}\right) \times 20
\]

Simplifying the equation:
\[
960 = N \times 2.4
\]

\[
N = \frac{960}{2.4} = 400
\]

So, the number of shares is **400**. However, this is not listed as one of the options. It may be possible the dividend or income given has a typo. 

---

### Question 2:
**Aritra opened an RD account in PNB for 20 months. If the rate of interest is 9% per annum and he received ₹441 as interest, the monthly installment is:**

We use the formula for Recurring Deposit interest:

\[
I = P \times \frac{n(n+1)}{2} \times \frac{r}{12 \times 100}
\]

Where:
- \( I = 441 \) (interest earned)
- \( n = 20 \) months (tenure)
- \( r = 9\% \) annual interest rate
- \( P \) is the monthly installment

Substitute the known values:

\[
441 = P \times \frac{20(21)}{2} \times \frac{9}{12 \times 100}
\]

Simplify the equation:

\[
441 = P \times 210 \times \frac{9}{1200}
\]

\[
441 = P \times 1.575
\]

\[
P = \frac{441}{1.575} \approx 280
\]

So, the monthly installment is ₹280. The answer is (a) ₹280.

---

### Question 3:
**The solution set for the inequality \( 2x + 7 \leq 17, x \in \mathbb{N} \) is:**

First, solve the inequality:

\[
2x + 7 \leq 17
\]

Subtract 7 from both sides:

\[
2x \leq 10
\]

Divide by 2:

\[
x \leq 5
\]

Since \( x \in \mathbb{N} \) (natural numbers), the possible values of \( x \) are:
\[
x \in \{1, 2, 3, 4, 5\}
\]

The solution set is \( \{1, 2, 3, 4, 5\} \), which corresponds to option (b).

---

Would you like me to continue solving more questions, or do you want detailed explanations of any specific ones? Feel free to ask for further clarifications.

### Related Questions:
1. How can we adjust the calculation in question 1 if there's a different income value?
2. What is the concept of recurring deposit interest calculations?
3. How do you solve inequalities with natural number constraints?
4. What are the general properties of dividend income?
5. How can you check if interest rates change the installment value in RD problems?

**Tip**: Always verify your units when calculating financial problems to ensure consistency.

Marish has some shares of ₹20 of a company paying 12% dividend. If his annual income is ₹9600, then the number of shares he bought?

Learn how to calculate the number of shares based on the annual income and dividend rate using the formula for dividend income. This problem involves basic algebra and percentage calculations, suitable for Grade 10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation