A sum of Rs 4000 becomes Rs 7000 in 6 years at simple interest. If the rate of interest becomes double of itself, then what will be the amount (in Rs) after 6 years?

Options

A. 8500
B. 9000
C. 8000
D. 10000

Answer

To solve the problem step by step, we will follow the principles of simple interest.

### Step 1: Identify the given values
- Principal (P) = Rs 4000
- Amount (A) after 6 years = Rs 7000
- Time (T) = 6 years

### Step 2: Calculate the Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = A - P \]
Substituting the known values:
\[ SI = 7000 - 4000 = 3000 \]

### Step 3: Calculate the Rate of Interest (R)
We know the formula for Simple Interest:
\[ SI = \frac{P \times R \times T}{100} \]
Rearranging to find R:
\[ R = \frac{SI \times 100}{P \times T} \]
Substituting the known values:
\[ R = \frac{3000 \times 100}{4000 \times 6} \]
Calculating the right-hand side:
\[ R = \frac{300000}{24000} = 12.5\% \]

### Step 4: Determine the new rate of interest
If the rate of interest becomes double:
\[ New\ Rate = 2R = 2 \times 12.5\% = 25\% \]

### Step 5: Calculate the new Simple Interest with the doubled rate
Using the new rate, we will calculate the new Simple Interest for the same principal and time:
\[ New\ SI = \frac{P \times New\ Rate \times T}{100} \]
Substituting the known values:
\[ New\ SI = \frac{4000 \times 25 \times 6}{100} \]
Calculating:
\[ New\ SI = \frac{600000}{100} = 6000 \]

### Step 6: Calculate the new amount after 6 years
The new amount (A') after 6 years with the new Simple Interest will be:
\[ A' = P + New\ SI \]
Substituting the values:
\[ A' = 4000 + 6000 = 10000 \]

### Final Answer
The amount after 6 years, when the rate of interest is doubled, will be Rs 10,000.

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