Question

Find the true discount, Banker's discount
and Banker's gain on a bill of Rs 4,240 due
6 months hence at 9% pa​

Answer 1

Given:

A bill of Rs 4,240 due  6 months hence at 9% p.a​.

To find:

True discount, Banker's discount  and Banker's gain

Solution:

Sum due, S.D. = Rs. 4240

Time period, n = $\frac{6}{12} = \frac{1}{2} \:year$

The rate of interest, R = 9% p.a.

Finding the Banker's discount:

We have the formula as:

$\boxed{\bold{B.D. = \frac{S.D \times n\times R }{100} }}$

Substituting the values, we get

$\bold{B.D.} = \frac{4240 \times 9\times \frac{6}{12} }{100} = \frac{4240 \times 9\times 0.5 }{100} = \frac{19080 }{100} = \bold{Rs.\:190.80}$

Finding the True discount:

We have the formula as:

$\boxed{\bold{B.D. = T.D.( 1 + \frac{ n\times R }{100} )}}$

Substituting the values of B.D., n & R, we get

$190.80 = T.D. (1 + \frac{ 9\times \frac{6}{12} }{100} )$

$\implies 190.80 = T.D. (1 + \frac{ 9\times 0.5 }{100} )$

$\implies 190.80 = T.D. (1 + 0.045)$

$\implies 190.80 = T.D. \times 1.045$

$\implies T.D. = \frac{190.80}{1.045}$

$\implies \bold{T.D. = Rs.\:182.58}$

Finding the Banker's gain:

We have the formula as:

$\boxed{\bold{B.G. = B.D. - T.D.}}$

Substituting the value of B.D. & T.D., we get

$\bold{B.G.} = 190.80 - 182.58 = \bold{Rs. \:8.22}$

Thus,

$\boxed{\bold{True \:Discount \rightarrow\: \underline{Rs. \:182.58}}}\\\\\boxed{\bold{Banker's \:Discount \rightarrow\: \underline{Rs.\: 190.80}}}\\\boxed{\bold{Banker's \:Gain \rightarrow\: \underline{Rs. 8.22}}}$

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