Study the following table charts carefully and answer the questions given beside. the following table shows the principal amount invested by five different person ins a scheme and the number of years and the rate of interest they are provided for the investment and the simple interest they earned after a certain period also given. Some values are missing

Please read the question carefully and select the best choice to fill in the blank.

If the simple interest earned by C is Rs. 4000 less than the simple interest earn by A.

Then find the number of year. A invested the amount.

OPTIONS




PERSONS

PRINCIPLE

NUMBER

OF

YEARS(N)

RATE OF

INTEREST (R79)

SIMPLE

INTEREST

A

75000




12%










3




28800




90000

4

10%

36000

D




6

8%







E

40000

2







4.4 Years

5.6 Years

6 years

8.5 years

To solve the problem, we need to find the number of years \( N_A \) that A invested his amount, given that the simple interest (SI) earned by C is Rs. 4,000 less than the simple interest earned by A.

### Step 1: Recall the formula for simple interest
The formula for calculating simple interest is:
\[
SI = \frac{P \times R \times N}{100}
\]
where:
- \( P \) is the principal amount,
- \( R \) is the rate of interest per annum, and
- \( N \) is the number of years.

### Step 2: Known values for person A
From the table, we are given:
- Principal invested by A: \( P_A = 75,000 \)
- Rate of interest for A: \( R_A = 12\% \)
- Simple interest earned by A: \( SI_A \) (unknown, but we will calculate it).

The simple interest for A is given by the formula:
\[
SI_A = \frac{P_A \times R_A \times N_A}{100}
\]
Substitute the known values:
\[
SI_A = \frac{75,000 \times 12 \times N_A}{100} = 9,000 \times N_A
\]
Thus, the simple interest for A is:
\[
SI_A = 9,000 \times N_A
\]

### Step 3: Known values for person C
For person C, we are given:
- Principal invested by C: \( P_C = 90,000 \)
- Number of years for C: \( N_C = 4 \)
- Rate of interest for C: \( R_C = 10\% \)
- Simple interest earned by C: \( SI_C = 36,000 \) (from the table).

The simple interest for C can be calculated using the same formula:
\[
SI_C = \frac{P_C \times R_C \times N_C}{100} = \frac{90,000 \times 10 \times 4}{100} = 36,000
\]

### Step 4: Use the relation between \( SI_A \) and \( SI_C \)
We are given that the simple interest earned by C is Rs. 4,000 less than the simple interest earned by A. So, we can write:
\[
SI_A = SI_C + 4,000
\]
Substitute \( SI_C = 36,000 \) into the equation:
\[
SI_A = 36,000 + 4,000 = 40,000
\]

### Step 5: Solve for \( N_A \)
Now, we know that \( SI_A = 40,000 \), and from Step 2, we have:
\[
SI_A = 9,000 \times N_A
\]
Equating the two expressions for \( SI_A \):
\[
9,000 \times N_A = 40,000
\]
Solve for \( N_A \):
\[
N_A = \frac{40,000}{9,000} \approx 4.44 \text{ years}
\]

### Step 6: Compare with the given options
The closest option to \( N_A \approx 4.44 \) years is **4.4 years**.

### Final Answer:
The number of years A invested the amount is **4.4 years**.

---

Would you like further clarifications on any steps? Here are 5 related questions for practice:

1. How would the result change if A had invested Rs. 80,000 instead of Rs. 75,000?
2. What would be the simple interest earned by A if he had invested for 6 years at 12%?
3. How does changing the rate of interest affect the simple interest earned over time?
4. What is the total interest earned by all five persons together?
5. If C had invested for 5 years instead of 4, what would his new simple interest be?

**Tip:** For word problems, start by organizing known values and equations clearly to simplify your calculations.

Learn how to calculate simple interest with a detailed problem-solving approach. Solve for the number of years A invested his amount given the principal amount, rate of interest, and known simple interest values. Suitable for students in Grades 9-12.

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