Question

If the 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 conditions?
(i) 300 rupees
(ii) 1000 rupees
(iii) 700 rupees
(iv) 500 rupees

Answer 1

Hint: We first assume the rate of interest and the number of years the principal amount has been under. We use the formula given by $a=\dfrac{pnr}{100}$ to relate the principal and the interest. We find the multiplied values of the variable from the first condition. We use that to find the solution of the problem from the next condition.

Complete step by step answer:
Let the interest on 3000 rupees is 600 rupees at a certain rate for a certain number of years.
Let the years be n and the interest rate be r.
We know that if the principal amount be p and the amount of interest is a, then the formula of finding the interest is defined by $a=\dfrac{pnr}{100}$.
For our given problem it’s given the interest on 3000 rupees is 600 rupees at a rate of r for n years.
We put the values $a=600,p=3000$ in the equation $a=\dfrac{pnr}{100}$.
We get $600=\dfrac{3000\times nr}{100}$. Solving the equation, we get the value of $nr$.
$\begin{align}
  & 600=\dfrac{3000nr}{100} \\
 & \Rightarrow nr=\dfrac{100\times 600}{3000}=20 \\
\end{align}$
Now we have to find the interest on 1500 rupees at a rate of r for n years. The rate of interest and the time frame hasn’t been changed.
Let the interest be y. Then $y=\dfrac{pnr}{100}$. Here p will be 1500.
So, $y=\dfrac{1500\times 20}{100}=300$.
Therefore, the interest on 1500 rupees under the same conditions will be 300 Rs.

So, the correct answer is “Option (i)”.

Note: We need to always use simple interest if otherwise mentioned. The formula for simple interest and compound interest is totally different. The solution would have been different if we had used compound interest. The relation between principal and the interest is linearly dependent when other things like time and rate are constant.