Answer  Hint: We will assume the sum invested as x rupees. We have been given that it becomes triple after 3 years which means it becomes 3 x. Now, we know that the final amount = principal amount + simple interest. So, we will find the simple interest from that and using the formula, $\text{simple interest}=\dfrac{\text{principal amount}\times \text{time}\times \text{rate}}{100}$, we will find the rate of interest. Complete step-by-step answer: We are given the time period as 16 years and that the sum becomes triple after 16 years. So, we will first assume the sum invested as Rs. x. We have been given that after 16 years, it becomes triple, so,Final amount = $3\times x=3x$.Now, we know that the final amount is the summation of the principal amount and simple interest,Final amount = principal amount + simple interest, which can be written as,3 x = x + simple interest, so we get the simple interest as = 3 x - x = 2 x.Now, we have the principal amount, time and the simple interest, so we will find the rate using the formula, $\text{simple interest}=\dfrac{\text{principal amount}\times \text{time}\times \text{rate}}{100}$. So, by substituting the values of the parameters we get,$\begin{align} & \dfrac{2x}{1}=\dfrac{x\times 16\times rate}{100} \\ & \Rightarrow \dfrac{2}{1}=\dfrac{16\times rate}{100} \\ \end{align}$ On cross-multiplying, we get,$\begin{align} & rate=\dfrac{2\times 100}{16} \\ & \Rightarrow rate=12.5\% \\ \end{align}$ Hence, we get the rate of interest as 12.5 %.Note: There is a possibility that the students think that the simple interest becomes triple of the principal amount, that is simple interest is 3 x. So, in further calculations for finding the rate of interest, they will end up with, $rate=\dfrac{3\times 100}{16}\Rightarrow 18.75\%$. But students should read the question carefully to understand that the sum becomes triple, which means the principal amount becomes triple after 16 years.
36. The interest on a certain sum of money is ₹ 22 and the discount on the same sum for the same time and at the same rate is ₹ 20, find the sum.
A. ₹ 220
100 Questions 100 Marks 60 Mins
Given: A certain sum of money becomes 25 times of itself in a span of 50 years on simple interest. Formula: r = (100 × SI)/(P × t) SI = A – P Where, SI → Simple interest A → Amount P → Principal r → rate t → time Calculation: Let the sum of money be P Amount becomes 25 times = 25P SI = 25P – P ⇒ 24P r = (100 × 24P)/(P × 50) ⇒ 2400P/50P ⇒ 2400/50 ⇒ 48 ∴ The rate of interest is 48% India’s #1 Learning Platform Start Complete Exam Preparation
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At what rate percent and amount of money becomes 25 times of itself in 25 years at simple interest
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