The true discount on a bill due 10 months hence at `6%` per annum is Rs. `26cdot25`. The amount of the bill is-

Options

A. Rs. 1575
B. Rs 500
C. Rs.` 650cdot25`
D. Rs.` 551cdot25`

Answer

To find the amount of the bill given the true discount, we can use the formula for true discount (TD):

\[ TD = \frac{P \times R \times T}{100 \times 12} \]

Where:
- \( TD \) is the true discount,
- \( P \) is the present value (the amount of the bill),
- \( R \) is the rate of interest per annum,
- \( T \) is the time in months.

Given:
- \( TD = 26.25 \)
- \( R = 6\% \)
- \( T = 10 \) months

Now, we can rearrange the formula to find \( P \):

\[ P = \frac{TD \times 100 \times 12}{R \times T} \]

Substituting the values into the equation:

\[ P = \frac{26.25 \times 100 \times 12}{6 \times 10} \]

Calculating the numerator:

\[ 26.25 \times 100 \times 12 = 31500 \]

Calculating the denominator:

\[ 6 \times 10 = 60 \]

Now, substituting back into the equation for \( P \):

\[ P = \frac{31500}{60} \]

Calculating \( P \):

\[ P = 525 \]

Thus, the amount of the bill is Rs. 525.

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