Discussion
If the true discount on a sum due 2 years hence at 14% per annum is ₹168, what is the sum due?
Answer: B
Correct answer: ₹768
Apply \[ \text{TD} = \frac{A \times RT}{100 + RT} \] with \( RT = 14 \times 2 = 28 \): \[ 168 = \frac{A \times 28}{128} \;\Rightarrow\; A = \frac{168 \times 128}{28} = 6 \times 128 = 768. \] The arithmetic simplifies neatly because \( 168/28 = 6 \), which is worth looking for before multiplying out. Checking: the present worth is \( 768 - 168 = 600 \), and the simple interest on 600 at 14% for 2 years is \( 600 \times 0.28 = 168 \) - the true discount as given. For completeness, the banker’s discount would be interest on the face value, \( 768 \times 0.28 = 215.04 \), and the banker’s gain the difference, 47.04 - which is also the interest on the true discount, \( 168 \times 0.28 \). The distractor 800 is the answer obtained by wrongly treating TD as interest on the face value.
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