Discussion
The true discount on ₹1,760 due after a certain time at 12% per annum is ₹160. What is the time?
Answer: A
Correct answer: 10 months
The present worth is \( 1760 - 160 = 1600 \), and the true discount is the simple interest on it: \[ 160 = \frac{1600 \times 12 \times T}{100} = 192T \;\Rightarrow\; T = \frac{160}{192} = \frac{5}{6}\text{ year}. \] Five sixths of a year is 10 months. The single step that decides the problem is subtracting the discount before applying the interest formula - TD is interest on the present worth, not on the face value. Using 1,760 would give \( T = 160 \times 100/(1760 \times 12) \approx 0.758 \) year, about 9.1 months, which is wrong but plausible enough to be offered as a trap in many versions of this question. Converting the fractional year to months at the end is the other place marks are lost: multiply by 12, not by 10.
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