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?
a. 300
b. 1000
c. 700
d. 500

Answer 1

Hint: In this question we have been given with two principal amounts and simple interest on one principal we need to calculate the simple interest on another principal, with the condition of same rate and time period. So, we don’t really need to calculate the rate and time. We can write the expression for one case and substitute that expression in another case.

Complete step-by-step answer:

The simple interest, SI is calculated on the basis of three important factors. The principal P is the amount that is borrowed/lent, the rate of interest R is the multiplication factor (in percent per annum) which is used to calculate the interest, the time T is the time period (in years) for which the amount is borrowed/lent. So, the final formula of calculating the simple interest is:
$SI=\dfrac{PRT}{100}............(i)$

We have been given: P = 3000, SI = 600. The R and T are unknowns for now.

Substituting the values in equation (i), we get
$\Rightarrow 600=\dfrac{3000\times R\times T}{100}$

On cross-multiplying we get,
$\Rightarrow 600\times 100=3000\times RT$
\[\begin{align}
  & \Rightarrow RT=\dfrac{600\times 100}{3000} \\
 & \Rightarrow RT=20.......................(ii) \\
\end{align}\]

Now, it is required to find out the simple interest on a principal of 1500 keeping other conditions same i.e., R and T both unchanged. So, using the formula from equation (i), we get
$SI=\dfrac{1500\times R\times T}{100}$

Substituting the value of ‘RT’ from equation (ii), we get
$\Rightarrow SI=\dfrac{1500\times 20}{100}$
$\Rightarrow SI=300$

Therefore, the simple interest on Rs.1500 is Rs.300.

Hence, the final answer is option (a).

Note: You must not get stuck to further solve the RT = 20, in order to find out both rate and time individually. The shortcut alternative way:
$\dfrac{SI}{600}=\dfrac{100\left( 1500RT \right)}{100\left( 3000RT \right)}$
$SI=\dfrac{600\left( 1500 \right)}{\left( 3000 \right)}=300$