Question

Gopi borrowed Rs. 1800 at 12% per annum for 2 years and Krishna borrowed Rs. 1200 at 18% per annum for 3 years. Then the ratio of interests paid by them is
(a) 1:2
(b) 2:3
(c) 3:1
(d) 2:1

Answer 1

Hint: We have to consider ${{I}_{1}}$ to be the interest paid by Gopi and ${{I}_{2}}$ to be the interest paid by Krishna. We will use the formula for simple interest, that is, $SI=\dfrac{P\times R\times T}{100}$ . We have to substitute for principal amount, rate of the interest and the time period in years in this formula for Gopi and Krishna. Then, we have to take the ratios of ${{I}_{1}}$ and ${{I}_{2}}$ .

Complete step-by-step solution:
We have to find the ratio of interests paid by Gopi and Krishna. Let the interest paid by Gopi be ${{I}_{1}}$ and that of Krishna be ${{I}_{2}}$ . We know that simple interest is the product of principal amount, rate and time period and is given by
$SI=\dfrac{P\times R\times T}{100}$
where P is the principal amount, R is the rate of the interest and T is the time period in years.
Let us find the simple interest paid by Gopi. We are given that principal amount, \[\text{P = Rs}\text{. 1800}\] , \[\text{R}=12\%\] and \[\text{T = 2 years}\] . Then, we can write ths SI as
${{I}_{1}}=\dfrac{1800\times 12\times 2}{100}$
Let us cancel the zeroes from 1800 and the denominator.
$\begin{align}
& \Rightarrow {{I}_{1}}=\dfrac{18\require{cancel}\cancel{00}\times 12\times 2}{1\require{cancel}\cancel{00}} \\
 & \Rightarrow {{I}_{1}}=18\times 12\times 2 \\
 & \Rightarrow {{I}_{1}}=Rs.432 \\
\end{align}$
Now, we have to find the simple interest paid by Krishna. We are given that principal amount, \[\text{P = Rs}\text{. 1200}\] , \[\text{R}=18\%\] and \[\text{T = 3 years}\] . Then, we can write ths SI as
${{I}_{2}}=\dfrac{1200\times 18\times 3}{100}$
Let us cancel the zeroes from 1800 and the denominator.
$\begin{align}
  & \Rightarrow {{I}_{2}}=\dfrac{12\require{cancel}\cancel{00}\times 18\times 3}{1\require{cancel}\cancel{00}} \\
 & \Rightarrow {{I}_{2}}=12\times 18\times 3 \\
 & \Rightarrow {{I}_{2}}=Rs.648 \\
\end{align}$
Now, we have to find the ratio of ${{I}_{1}}$ and ${{I}_{2}}$ .
$\Rightarrow \dfrac{{{I}_{1}}}{{{I}_{2}}}=\dfrac{432}{648}$
Let us cancel the common factor 6.
$\Rightarrow \dfrac{{{I}_{1}}}{{{I}_{2}}}=\dfrac{72}{108}$
We can again cancel the common factor 6.
$\Rightarrow \dfrac{{{I}_{1}}}{{{I}_{2}}}=\dfrac{12}{18}$
Let us cancel the common factor 6.
$\Rightarrow \dfrac{{{I}_{1}}}{{{I}_{2}}}=\dfrac{2}{3}$
Therefore, the ratio of the ratio of interests paid by Gopi and Krishna is 2:3.
Hence, the correct option is b.

Note: Students must be thorough with the formulas of simple interest (SI) and compound interest (CI). In the above solution, we have used SI instead of CI because SI is used when we have calculated interest based on the principal amount of a loan or deposit. We will use CI when we have to calculate interest based on the principal amount and the interest that accumulates on it in every period.