In 4 years. Rs 6000 amounts to Rs 8,000. In what time at the same rate will Rs 525 amount to Rs 700 ?

Options

A. 5 years
B. 3 years
C. 4 years
D. None of these

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Understand the Given Information
We know that in 4 years, Rs. 6000 amounts to Rs. 8000.

- Principal (P) = Rs. 6000
- Amount (A) = Rs. 8000
- Time (T) = 4 years

### Step 2: Calculate the Simple Interest (SI)
Simple Interest can be calculated using the formula:
\[ \text{SI} = \text{Amount} - \text{Principal} \]

So,
\[ \text{SI} = 8000 - 6000 = 2000 \]

### Step 3: Calculate the Annual Simple Interest
Since the simple interest of Rs. 2000 is earned in 4 years, we can find the interest earned in 1 year:
\[ \text{SI per year} = \frac{2000}{4} = 500 \]

### Step 4: Calculate the Rate of Interest (R)
Now, we can find the rate of interest using the formula:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

Rearranging the formula to find R:
\[ R = \frac{\text{SI} \times 100}{P \times T} \]

Substituting the values:
\[ R = \frac{500 \times 100}{6000 \times 1} = \frac{50000}{6000} = \frac{25}{3} \% \]

### Step 5: Set Up the Second Case
Now we need to find out how long it will take for Rs. 525 to amount to Rs. 700 at the same rate of interest.

- New Principal (P) = Rs. 525
- New Amount (A) = Rs. 700

### Step 6: Calculate the New Simple Interest (SI)
Using the same formula for SI:
\[ \text{SI} = A - P = 700 - 525 = 175 \]

### Step 7: Use the SI Formula to Find Time (T)
Using the SI formula again:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

Rearranging to find T:
\[ T = \frac{\text{SI} \times 100}{P \times R} \]

Substituting the values:
\[ T = \frac{175 \times 100}{525 \times \frac{25}{3}} \]

### Step 8: Simplify the Equation
Calculating the denominator:
\[ 525 \times \frac{25}{3} = \frac{13125}{3} = 4375 \]

Now substituting back into the equation for T:
\[ T = \frac{17500}{4375} \]

### Step 9: Perform the Division
Now we can simplify:
\[ T = 4 \text{ years} \]

### Final Answer
Thus, it will take **4 years** for Rs. 525 to amount to Rs. 700 at the same rate of interest.

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