In 5 years, Rs. 5000 amounts to Rs. 9000. In what time at the same rate will Rs. 600 amount to Rs. 900?

Options

A. a)5.5 years
B. b)3.125 years
C. c)6.3 years
D. d)2.4 years

Explanation

To solve the problem step by step, we will first determine the rate of interest based on the information given, and then use that rate to find the time required for Rs. 600 to amount to Rs. 900.

### Step 1: Calculate the Simple Interest
We know that in 5 years, Rs. 5000 amounts to Rs. 9000.

To find the simple interest (SI), we subtract the principal (P) from the amount (A):
\[ SI = A - P = 9000 - 5000 = 4000 \]

### Step 2: Use the Simple Interest Formula to Find the Rate
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(SI\) = Simple Interest
- \(P\) = Principal
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

We can rearrange this formula to solve for \(R\):
\[ R = \frac{SI \times 100}{P \times T} \]

Substituting the values we have:
- \(SI = 4000\)
- \(P = 5000\)
- \(T = 5\)

Now substituting these values into the formula:
\[ R = \frac{4000 \times 100}{5000 \times 5} \]

Calculating the right side:
\[ R = \frac{400000}{25000} = 16\% \]

### Step 3: Calculate the Simple Interest for Rs. 600
Now we need to find out how long it will take for Rs. 600 to amount to Rs. 900.

First, we calculate the simple interest for this case:
\[ SI = A - P = 900 - 600 = 300 \]

### Step 4: Use the Simple Interest Formula to Find the Time
Using the same simple interest formula:
\[ SI = \frac{P \times R \times T}{100} \]
We can rearrange it to solve for \(T\):
\[ T = \frac{SI \times 100}{P \times R} \]

Substituting the values:
- \(SI = 300\)
- \(P = 600\)
- \(R = 16\)

Now substituting these values into the formula:
\[ T = \frac{300 \times 100}{600 \times 16} \]

Calculating the right side:
\[ T = \frac{30000}{9600} = 3.125 \text{ years} \]

### Final Answer
The time required for Rs. 600 to amount to Rs. 900 at the same rate is **3.125 years**.

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