Question

In 4 years, Rs. 6000 amounts to Rs. 8000. In what time at the same rate will Rs. 525 amount to Rs. 700?

• A. 2 years
• B. 3 years
• C. 4 years
• D. 5 years

Hint:

Find the rate from the first case using SI = PRT/100, then apply the same rate to the second case and solve for time.

Answer 1

The Correct Option is C

Step 1: Find the simple interest and rate from the first case.
Simple interest \(SI = A - P = 8000 - 6000 = Rs.\ 2000\) over 4 years on a principal of Rs. 6000. Using \(SI = \dfrac{P \times R \times T}{100}\), we get \(2000 = \dfrac{6000 \times R \times 4}{100}\), so \(R = \dfrac{2000 \times 100}{6000 \times 4} = \dfrac{25}{3}\%\) per year.

Step 2: Set up the second case with this rate.
Here principal \(P = 525\), amount \(A = 700\), so \(SI = 700 - 525 = Rs.\ 175\).

Step 3: Solve for the unknown time.
Using the same formula, \(175 = \dfrac{525 \times \frac{25}{3} \times T}{100}\). Simplify the right side: \(525 \times \dfrac{25}{3} = 4375\), so \(175 = \dfrac{4375 \times T}{100}\), giving \(T = \dfrac{175 \times 100}{4375} = 4\) years.

Step 4: Check the other options.
2, 3, and 5 years do not satisfy \(175 = \dfrac{4375 \times T}{100}\); only \(T = 4\) balances the equation exactly.

Final Answer:
Rs. 525 grows to Rs. 700 at this rate in 4 years. \[ \boxed{4 \text{ years}} \]