Question : Kanchan lent INR 10,000 for 2 years and INR 5,000 for 4 years at the same rate of simple interest. If the total interest received by Kanchan is INR 2,000, then what was the rate of interest?
Option 1: 5%
Option 2: 2%
Option 3: 3%
Option 4: 4%
Correct Answer: 5%
Solution :
Let's denote the rate of interest as $R$.
The simple interest (SI) can be calculated using the formula $SI=\frac{P×R×T}{100}$, where P is the principal amount, R is the rate of interest, and T is the time in years.
For the first loan of INR 10,000 for 2 years: $SI_1=\frac{10,000×R×2}{100}$
For the second loan of INR 5,000 for 4 years: $SI_2=\frac{5,000×R×4}{100}$
Also,
The total interest received is the sum of the interest from both loans: $SI_1+SI_2=\frac{10,000×R×2}{100}+\frac{5,000×R×4}{100}$
Given that the total interest is INR 2,000: $\frac{10,000×R×2}{100}+\frac{5,000×R×4}{100}=2000$
⇒ $200×R+200×R=2,000$
⇒ $400×R=2,000$
⇒ $R=5\%$
Hence, the correct answer is 5%.
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