Question

A specific amount of money is loaned out at a simple interest rate, resulting in ₹15,000 in 2 years and ₹20,000 in 4 years. The rate percentage per annum is:

• A. 25%
• B. 20%
• C. 18%
• D. 15%

Answer 1

Answer:

A. 25%

Let the principal be (P) and rate be (r%).

Using Simple Interest:

Amount after 2 years:
$P + 2r\% \text{ of } P = 15000$

Amount after 4 years:
$P + 4r\% \text{ of } P = 20000$

Subtract the equations:

$(P + 4r$

$2r\%P = 5000$

$\frac{2r}{100}P = 5000$
$\Rightarrow \frac{rP}{50} = 5000$
$\Rightarrow rP = 250000$

Now use first equation:

$P + \frac{2r}{100}P = 15000$
$\Rightarrow P + \frac{rP}{50} = 15000$

Substitute (rP = 250000):

$P + \frac{250000}{50} = 15000$
$\Rightarrow P + 5000 = 15000$
$\Rightarrow P = 10000$

Find rate:

$rP = 250000$
$\Rightarrow r \times 10000 = 250000$
$\Rightarrow r = 25$

Final Answer:

25% per annum