Question

The B.G. on a bill due 6 months hence is Rs.100, the rate of interest being $10\% $p.a. Find the face value (in Rs.) of the bill.
A. 42000
B. 24000
C. 21000
D. 46000

Answer 1

Hint: Find the rate of the interest in simple form, convert the time into years and use the formula for banker gain, which is equal to the product of total discount, time and rate.

Complete step-by-step solution:
Given: B.G. on bill due 6 months is Rs.100 and the rate of interest is $10\% $ p.a.
Rate of interest is $10\% $ p.a. \[ = 0.1\].
Given time is 6 months, convert it into the form of years by dividing it by 12, as the number of months in a year are 12 and denote the time by $t$.
Thus, \[t = \dfrac{6}{{12}} = \dfrac{1}{2}\]years
The B.G. is the interest on T.D.
${\text{B}}{\text{.G = T}}{\text{.D}}{\text{. }} \times {\text{ Time }} \times {\text{ R}}$
Substitute 100 for B.G, $\dfrac{1}{2}$ for time $t$ and $0.1$ for ${\text{R}}$ in the above formula.
\[100 = {\text{T}}{\text{.D}}{\text{.}} \times \dfrac{1}{2} \times 0.1\]
Solve for T.D.
\[{\text{T}}{\text{.D}}{\text{.}} = \dfrac{{200}}{{0.1}} = 2000\]
Find the bankers discount by adding the values of T.D and B.G. and denote is by B.D.
\[{\text{B}}{\text{.D}}{\text{.}} = 2000 + 100 = 2100\]
Now, we have a formula of face value \[
  {\text{ = }}\dfrac{{B.D \times T.D}}{{B.G.}} \\
   \\
\]\[
   = \dfrac{{2100 \times 2000}}{{100}} \\
   \\
\]\[ = 42000\]
Hence the face value will be Rs. 42000.
Therefore, option (A) is correct.

Note: Bankers discount is also required to find the face value, so we also need to find the value of T.D and B.G., as it is the sum of T.D and B.G.: Bankers discount is also required to find the face value, so we also need to find the value of T.D and B.G., as it is the sum of T.D and B.G.