Rs 5,000 amounts to Rs 5,700 in one year. AC cordingly, what will be the amount ₹ 7,000 become at same rate of simple interest in 5 years?

Options

A. Rs 12,700
B. Rs 77,00
C. Rs 10,500
D. Rs 11,900

Answer

To solve the problem step by step, we will follow the process of calculating simple interest and then finding the final amount.

### Step 1: Identify the Principal and Amount from the First Case
- Principal (P) = Rs 5,000
- Amount (A) = Rs 5,700

### Step 2: Calculate the Simple Interest (SI) for the First Case
Using the formula for Simple Interest:
\[ \text{Simple Interest (SI)} = \text{Amount} - \text{Principal} \]
\[ \text{SI} = 5,700 - 5,000 = 700 \]
So, the Simple Interest for one year is Rs 700.

### Step 3: Use the Simple Interest Formula to Find the Rate of Interest (R)
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of Interest
- T = Time in years

Substituting the known values:
\[ 700 = \frac{5,000 \times R \times 1}{100} \]

### Step 4: Solve for R
Rearranging the equation to find R:
\[ 700 = \frac{5,000R}{100} \]
\[ 700 \times 100 = 5,000R \]
\[ 70,000 = 5,000R \]
\[ R = \frac{70,000}{5,000} = 14 \]
So, the rate of interest (R) is 14%.

### Step 5: Calculate the Simple Interest for the Second Case
Now we need to find the amount for a principal of Rs 7,000 over 5 years at the same rate of interest (14%).
Using the Simple Interest formula again:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- P = Rs 7,000
- R = 14%
- T = 5 years

Substituting the values:
\[ \text{SI} = \frac{7,000 \times 14 \times 5}{100} \]

### Step 6: Calculate the Simple Interest
Calculating the above expression:
\[ \text{SI} = \frac{7,000 \times 14 \times 5}{100} = \frac{490,000}{100} = 4,900 \]
So, the Simple Interest for 5 years is Rs 4,900.

### Step 7: Calculate the Total Amount
Finally, we calculate the total amount (A) using the formula:
\[ \text{Amount (A)} = \text{Principal} + \text{Simple Interest} \]
\[ A = 7,000 + 4,900 = 11,900 \]

### Final Answer
The amount that Rs 7,000 will become at the same rate of simple interest in 5 years is **Rs 11,900**.

---