Discussion
The true discount on ₹1,860 due after a certain time at 5% per annum is ₹60. What is the time?
Answer: B
Correct answer: 8 months
First find the present worth, since the true discount is interest on that rather than on the face value: \[ \text{PW} = 1860 - 60 = 1800. \] Now apply the simple interest formula to the present worth: \[ 60 = \frac{1800 \times 5 \times T}{100} = 90T \;\Rightarrow\; T = \frac{60}{90} = \frac{2}{3}\text{ year}, \] which is 8 months. The single step that decides this problem is subtracting the discount before applying the interest formula. Using the face value of 1,860 instead gives \( T = 60 \times 100/(1860 \times 5) = 0.645 \) year, about 7.7 months - close enough to look plausible and wrong. The general form is \( \text{TD} = \dfrac{\text{PW} \times R \times T}{100} \), and remembering that PW rather than \( A \) appears in it settles most questions in this topic.
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