Question

In how many years shall Rs. 3,500 invested at the rate of 10% simple interest per annum, amount to Rs. 4,500?

• A. 2$\frac{4}{7}$ years
• B. 2$\frac{3}{7}$ years
• C. 2$\frac{6}{7}$ years
• D. 2$\frac{5}{7}$ years

Hint:

Quickly calculate the interest: \( 4500 - 3500 = 1000 \).
Since the interest rate is $10%$ per annum, the interest earned in one year is $10%$ of \( 3500 = 350 \).
To find the total number of years, divide the total interest by the interest earned in one year:
\[ T = \frac{1000}{350} = \frac{20}{7} = 2\frac{6}{7}\text{ years} \]
This is highly intuitive and avoids formulas.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
In this problem, we are given the Principal sum, the final Amount, and the annual rate of simple interest.
Our task is to find the duration or time period (in years) required for this growth to occur.
We will calculate the interest earned first and then apply the standard Simple Interest formula to solve for time.

Step 2: Key Formula or Approach:

• Simple Interest ($SI$) is the difference between the final Amount ($A$) and the Principal ($P$): \( SI = A - P \).
  
• The standard Simple Interest formula is: \( SI = \frac{P \times R \times T}{100} \).
  
• Rearranging the formula to solve for Time ($T$): \( T = \frac{SI \times 100}{P \times R} \).
  

Step 3: Detailed Explanation:

• Identify and write down the given values from the question:
  
• Principal ($P$) = $\text{Rs. } 3500$
  
• Amount ($A$) = $\text{Rs. } 4500$
  
• Rate of Interest ($R$) = $10%$ per annum
  
• Calculate the total Simple Interest ($SI$) earned on the investment:
  \[ SI = A - P = 4500 - 3500 = \text{Rs. } 1000 \]
  
• Now, use the Simple Interest formula to express the relation between $SI$, $P$, $R$, and $T$:
  \[ 1000 = \frac{3500 \times 10 \times T}{100} \]
  
• Simplify the expression on the right-hand side by canceling the zeros:
  \[ 1000 = \frac{35000 \times T}{100} \]
  \[ 1000 = 350 \times T \]
  
• Solve for the time period $T$ by dividing both sides by $350$:
  \[ T = \frac{1000}{350} \]
  
• Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is $50$:
  \[ T = \frac{1000 \div 50}{350 \div 50} = \frac{20}{7}\text{ years} \]
  
• Convert the improper fraction $\frac{20}{7}$ into a mixed fraction:
  \[ 20 = 7 \times 2 + 6 \]
  \[ T = 2\frac{6}{7}\text{ years} \]
  
• Thus, the time required is $2\frac{6}{7}\text{ years}$.
  

Step 4: Final Answer:
The time required for Rs. 3,500 to amount to Rs. 4,500 at a 10% interest rate is $2\frac{6}{7}\text{ years}$, which corresponds to Option (C).