Question

The difference between compound interest and simple interest for 3 years at the rate of 20% per annum is ₹240. What is the principal lent?

• A. ₹1,675
• B. ₹1,875
• C. ₹1,975
• D. ₹1,775

Answer 1

Answer:

B. ₹1,875

The principal lent is ₹1,875.

• Difference between CI and SI = ₹240

• Rate of Interest ($R$) = 20%

• Time ($n$) = 3 years

$\text{Difference} = P \times \left(\frac{R}{100}\right)^2 \times \left(3 + \frac{R}{100}\right)$

1. Substitute the given values into the formula:
   $240 = P \times \left(\frac{20}{100}\right)^2 \times \left(3 + \frac{20}{100}\right)$

2. Simplify the fractions:
   $240 = P \times \left(\frac{1}{5}\right)^2 \times \left(3 + \frac{1}{5}\right)$
   $240 = P \times \left(\frac{1}{25}\right) \times \left(\frac{16}{5}\right)$
   $240 = P \times \frac{16}{125}$

3. Solve for Principal ($P$):
   $P = \frac{240 \times 125}{16}$
   $P = 15 \times 125$
   $P = \mathbf{1,875}$