Solution Breakdown

The question asks for the time required for a sum to reach ₹3,015 at a 5% simple interest rate, given information about its growth over 6 years.

Step 1: Calculate the Principal Sum (P)

We use the formula for the Amount (A) in simple interest: $A = P \left(1 + \frac{R \times T}{100}\right)$.

• Given: Amount (A) = ₹2,613, Rate (R) = 5%, Time (T) = 6 years.
• Substitute the values into the formula:

  ₹2,613 = P \left(1 + \frac{5 \times 6}{100}\right)

  ₹2,613 = P \left(1 + \frac{30}{100}\right)

  ₹2,613 = P (1 + 0.3)

  ₹2,613 = P (1.3)

• Solve for the Principal (P):

  P = \frac{₹2,613}{1.3}

  P = ₹2,010

The initial principal sum is ₹2,010.

Step 2: Calculate the Simple Interest (SI) for the Target Amount

We need the sum to amount to ₹3,015 at the same rate (5%). First, calculate the simple interest required for this amount.

• Principal (P) = ₹2,010
• Target Amount (A2) = ₹3,015
• Simple Interest (SI2) = A2 - P
• SI2 = ₹3,015 - ₹2,010
• SI2 = ₹1,005

Step 3: Calculate the Time (T2) for the Target Amount

Use the simple interest formula $SI = \frac{P \times R \times T}{100}$ to find the time (T2).

• We have SI2 = ₹1,005, P = ₹2,010, R = 5%.
• ₹1,005 = \frac{₹2,010 \times 5 \times T2}{100}
• ₹1,005 = \frac{10050 \times T2}{100}
• ₹1,005 = 100.5 \times T2
• Solve for T2:

  T2 = \frac{₹1,005}{100.5}

  T2 = 10

It will take 10 years for the sum to amount to ₹3,015.