Question

The rates of simple interest in Canara Bank and Punjab and Sind Bank are in the ratio 5:4. A person wants to deposit his total savings in two banks in such a way that he receives equal half yearly interest from both. He should deposit the savings in Canara Bank and Punjab and Sind Bank in the ratio
a. 2:5
b. 4:5
c. 5:2
d. 5:4

Answer 1

Hint: In order to solve this question, we will consider savings deposited in the Canara Bank and savings deposited in the Punjab and Sind Bank as X and Y respectively. Now, we will consider a term x such that 5x and 4x will become the rate of simple interest in Canara Bank and Punjab and Sind Bank respectively. Now, we will apply the formula of simple interest, that is, $I=\dfrac{PRT}{100}$ and will equate them to get the answer.

Complete step-by-step answer:
In this question, we have been asked to find the ratio of savings the person should invest in Canara Bank and Punjab and Sind Bank having interest ratio as 5:4 such that he receives equal half yearly interest from both.
To solve this, let us consider X and Y as the amount of savings deposited in the Canara Bank and in the Punjab and Sind Bank respectively. So, we can say that,
${{P}_{c}}=X$ and ${{P}_{p}}=Y$
Now, we will also consider x such that 5x and 4x will be the rates of interest in Canara Bank and Punjab and Sind Bank. So, we can say,
${{R}_{c}}=5x$ and ${{R}_{p}}=4x$
We have also been given that interest becomes equal after a time period of half year. So, we can say that time period of interest in both the banks is $\dfrac{1}{2}$ year, that is,
${{T}_{c}}=\dfrac{1}{2}yrs$ and ${{T}_{p}}=\dfrac{1}{2}yrs$
Now, we know that simple interest of any amount can be calculated by using the formula, $I=\dfrac{PRT}{100}$. And we have been given that interest becomes equal after $\dfrac{1}{2}$ year. So, we get,
$\begin{align}
  & {{I}_{c}}={{I}_{p}} \\
 & \dfrac{{{P}_{c}}\times {{R}_{c}}\times {{T}_{c}}}{100}=\dfrac{{{P}_{p}}\times {{R}_{p}}\times {{T}_{p}}}{100} \\
\end{align}$
Now, we will substitute the values in the above equation, so we get,
$\dfrac{\left( X \right)\left( 5x \right)\left( \dfrac{1}{2} \right)}{100}=\dfrac{\left( Y \right)\left( 4x \right)\left( \dfrac{1}{2} \right)}{100}$
Now, we will keep X and Y on one side and rest all on the other side. So, we get,
$\begin{align}
  & \dfrac{X}{Y}=\dfrac{\left( 4x \right)\left( \dfrac{1}{2} \right)\left( 100 \right)}{\left( 5x \right)\left( \dfrac{1}{2} \right)\left( 100 \right)} \\
 & \dfrac{X}{Y}=\dfrac{4}{5} \\
 & X:Y=4:5 \\
\end{align}$
Hence, we can say that the ratio of savings to be deposited in Canara and Punjab and Sind Bank should be 4:5. Therefore, we get option (b) as the correct answer.

Note: We can also solve this question without assuming a variable ‘x’, by directly assuming the ratios as 5 and 4 and after putting them in the formula of simple interest we can equate them to get the answer, that is X:Y. While solving this question, one can think of converting $\dfrac{1}{2}$ year into months but it is not at all needed as in both the cases the time period is in years.