Question

The true discount on a bill due 9 months hence at 16% per annum is Rs.189. The amount of the bill is:
A. Rs.1386
B. Rs.1764
C. Rs.1575
D. Rs.2268

Answer 1

Hint: Such type of question can be solved by using the formulas for True Discount (TD), Present worth (P). As the formula for True Discount or say Simple Interest is given by $TD = \dfrac{{PRN}}{{100}}$, where $R$ is the annual rate of Interest and N is the duration in year. Use this formula to obtain Present worth. After this amount of the bill is given by summation of Present worth and true discount means $SD = TD + P$.

Complete step-by-step solution:
Here given that the true discount on a bill due 9 months hence at 16% per annum is Rs.189.
So we can say that True discount $TD = 189$ Rs., Annual rate of interest $R = 16\% $ and period $N = 9$ months.
Firstly convert the period in year, so $N = \dfrac{9}{{12}} = \dfrac{3}{4}$ year.
We will use the formula for True discount or Simple interest $TD = \dfrac{{PRN}}{{100}}$ to find the value of Present worth.
So, $TD = \dfrac{{PRN}}{{100}}$
Now put the values of true discount, rate and period in the above equation,
So, $189 = \dfrac{{P \cdot 16 \cdot (\dfrac{3}{4})}}{{100}}$
Simplifying, $189 = \dfrac{{P \cdot 12}}{{100}}$
So, $P = \dfrac{{189 \cdot 100}}{{12}}$
Simplifying, $P = 1575$
So the present worth is $P = 1575$Rs.
Now we have to find the amount of the bill. It is also known as Sum due. Amount of bill or Sum due is given by the summation of Present worth and true discount.
So, $SD = TD + P$
Now putting the values of $TD = 189$ and $P = 1575$ in the above equation.
So, $SD = 189 + 1575$
Simplifying, $SD = 1764$
So the sum due or amount of the bill is 1764 Rs.

So, Option (B) is the correct answer.

Note: We can simplify the above calculation and directly use the formula $SD \cdot R \cdot N = TD(100 + RN)$ for the same calculation. Here put the values of True discount, rate and period in the equation to obtain the values of Sum due or amount of the bill.