Question & Answer
QUESTION

If the simple interest on 3000 rupees is 600 rupees at a certain rate for a certain number of years, what would the interest be on 1500 rupees under the same condition?
(a) 300 rupees
(b) 1000 rupees
(c) 700 rupees
(d) 500 rupees

ANSWER Verified Verified
- Hint: In this question, we first need to substitute the given values in the simple interest formula and get an equation. Then by assuming the simple interest in the next case as x and the rate and time as same in the first equation we get the second equation. Now, by dividing these two equations we get the result.



Complete step-by-step solution -

Simple interest is given by the formula:
\[SI=\dfrac{P\times T\times R}{100}\]
Where, P is the principal amount, R is the rate of interest, T is the duration and SI is the simple interest.
Now, in the given case let us assume the rate of the interest as R and the number of years as some T.
Given, that SI is 600 for a principal amount of 3000 which gives,
\[\begin{align}
  & SI=600 \\
 & P=3000 \\
\end{align}\]
Now, by substituting these values in the above simple interest formula we get,
\[\begin{align}
  & \Rightarrow SI=\dfrac{P\times T\times R}{100} \\
 & \Rightarrow 600=\dfrac{3000\times T\times R}{100} \\
\end{align}\]
Now, this on further simplification we get,
\[\Rightarrow 600=30\times T\times R......\left( 1 \right)\]
Now, let us assume that the simple interest in the next case as x.
Here, the value of R and T remains the same according to the given question.
Given, that the principal amount in this case was 1500 rupees.
\[\begin{align}
  & SI=x \\
 & P=1500 \\
\end{align}\]
Now, by substituting these values in the above simple interest formula we get,
\[\begin{align}
  & \Rightarrow SI=\dfrac{P\times T\times R}{100} \\
 & \Rightarrow x=\dfrac{1500\times T\times R}{100} \\
\end{align}\]
Now, this can be further simplified as.
\[\Rightarrow x=15\times T\times R......\left( 2 \right)\]
Let us now divide the equations (1) and (2)
\[\Rightarrow \dfrac{600}{x}=\dfrac{30\times T\times R}{15\times T\times R}\]
Now, on cancelling the common terms and further simplifying we get,
\[\Rightarrow \dfrac{600}{x}=2\]
Now, on rearranging the terms on both the sides we get,
\[\begin{align}
  & \Rightarrow x=\dfrac{600}{2} \\
 & \therefore x=300\text{ rupees} \\
\end{align}\]
Hence, the correct option is (a).

Note: Instead of dividing both the equations to get the simple interest in the second case we can calculate the value of \[T\times R\]from the first case and then substitute in the second case which directly gives the value of simple interest. Both the methods give the same result.
It is important to note that while calculating or simplifying we should not neglect any of the terms because as we are dividing the equations by neglecting any of the terms causes the unknown terms to be not cancelled. So, we cannot get the result.