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Last updated date: 04th Dec 2023
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MVSAT Dec 2023

Rihana took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period. Find the time period she has taken to return the loan-
1. 3.6 year
2. 6 years
3. 18 years
4. Cannot be determined

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Hint: This question involves 3 terms principle (P), rate (R), time (T). one of three are available in the question. Simple interest is also provided, put the value in the formula of simple interest, equate it and then proceed with the calculations.

Complete step-by-step answer:
Let the rate of interest R% and time = R years
Principle = Rs. 1200
Simple interest = Rs. 432
∴ S.I = \[\dfrac{{P \times R \times T}}{{100}}\]
\[ \Rightarrow 432 = \dfrac{{1200 \times R \times R}}{{100}}\]
\[ \Rightarrow \dfrac{{432 \times 100}}{{1200}} = {R^2}\]
\[ \Rightarrow {R^2} = \dfrac{{43200}}{{1200}}\]
\[ \Rightarrow {R^2} = 36\]
\[ \Rightarrow R = \sqrt {36} \]
\[ \Rightarrow R = 6\]
Therefore, the correct option is ‘B’ i.e. 6 years.

Note: Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by principal by the no. of days that elapsed between payments.