Question

The simple interest on Rs.400 for 8 months at 5 paise per rupee per month is
A. Rs.120
B. Rs.160
C. Rs.200
D. Rs.560

Answer 1

Hint: First of all we will convert the rate 5 paise per rupee per month into rupees per rupee per month. We will convert the paise into rupee by the following conversion;
1 paisa \[ = \dfrac{1}{{100}}{\rm{ rupee}}\]
Then, we will use the formula of simple interest as follows:
 \[S{\rm{ }}.{\rm{ I = P}} \times {\rm{R}} \times {\rm{T}}\]
Where, P is principal, R is rate and T is time.

Complete step-by-step answer:
We have been asked to find the simple interest of Rs.400 for 8 month at 5 paise per rupee per month.
So, we have, Principal \[\left( {\rm{P}} \right) = {\rm{Rs}}.{\rm{4}}00,{\rm{ Time}}\left( {\rm{T}} \right) = {\rm{8 month\ and\ Rate}}\left( {\rm{R}} \right) = {\rm{5 paise}}\] per rupee per month.
Now, we will have to convert the rate into rupee per rupee per month by using the conversion 1 paisa \[ = \dfrac{1}{{100}}{\rm{ rupee}}\].
Rate (R) \[ = \left( {\dfrac{5}{{100}}} \right)\]
 \[{\rm{ = }}\dfrac{1}{{20}}{\rm{ rupees\ per\ rupee\ per\ month}}\]

Now, we know that simple interest is given by,
 \[S{\rm{ }}.{\rm{ I = P}} \times {\rm{R}} \times {\rm{T}}\]
Where, P is principal, R is rate and T is time.
 \[\begin{array}{l}S{\rm{ }}{\rm{. I = 400}} \times \dfrac{1}{{20}} \times 8\\ \Rightarrow Rs.{\rm{ 160}}\end{array}\]
Therefore, the correct option is B.

Note: We might use the formula for SI as \[\dfrac{{PRT}}{{100}}\] but, in this formula, R is the rate of interest expressed as percentage. Considering our question, it is very important to convert the interest rate into rupee per rupee per month. Since, we have been given the principal value in rupee. Otherwise, we will get an incorrect answer. So, one must note that there is no need to divide by 100 in the formula while solving this particular question.