If Rs. 5,000 becomes Rs. 5,700 in a year time, what will Rs. 7,000 become at the end of 5 years at the same rate of simple interest?

Options

A. Rs.10,500
B. Rs. 11,900
C. Rs.12,700
D. Rs. 7,700

Answer

To solve the problem step by step, we will first determine the rate of simple interest from the information given and then use that rate to find out how much Rs. 7,000 will become at the end of 5 years.

### Step 1: Determine the Simple Interest Rate
We know that Rs. 5,000 becomes Rs. 5,700 in one year.

- **Principal (P)** = Rs. 5,000
- **Amount (A)** after 1 year = Rs. 5,700
- **Simple Interest (SI)** for 1 year = Amount - Principal = Rs. 5,700 - Rs. 5,000 = Rs. 700

Now, we can find the rate of interest using the formula for Simple Interest:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI \) = Simple Interest
- \( P \) = Principal
- \( R \) = Rate of interest
- \( T \) = Time in years

Since the time \( T \) is 1 year, we can rearrange the formula to find \( R \):
\[ R = \frac{SI \times 100}{P \times T} \]
Substituting the values:
\[ R = \frac{700 \times 100}{5000 \times 1} = \frac{70000}{5000} = 14\% \]

### Step 2: Calculate the Simple Interest for Rs. 7,000 over 5 Years
Now that we have the rate of interest, we can find out how much Rs. 7,000 will become at the end of 5 years.

- **Principal (P)** = Rs. 7,000
- **Rate (R)** = 14%
- **Time (T)** = 5 years

Using the same formula for Simple Interest:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the values:
\[ SI = \frac{7000 \times 14 \times 5}{100} \]
Calculating this:
\[ SI = \frac{7000 \times 70}{100} = \frac{490000}{100} = Rs. 4,900 \]

### Step 3: Calculate the Total Amount after 5 Years
Now we can find the total amount after 5 years:
\[ A = P + SI \]
Substituting the values:
\[ A = 7000 + 4900 = Rs. 11,900 \]

### Conclusion
Therefore, Rs. 7,000 will become Rs. 11,900 at the end of 5 years at the same rate of simple interest.