Discussion
The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is:
Answer: D
The present worth (PW) is what the sum is really worth today; the true discount (TD) is the interest that PW would earn over the remaining time:
\[ \text{Amount} = \text{PW}\left(1 + \frac{RT}{100}\right), \qquad \text{TD} = \text{Amount} - \text{PW} \]
\[ \text{PW} = 1760 - 160 = 1600 \]
The true discount is simple interest on the present worth, so
\[ 160 = \frac{1600 \times 12 \times T}{100} = 192\,T \]
\[ T = \frac{160}{192} = \frac{5}{6} \text{ year} = 10 \text{ months} \]
Note the interest is charged on the present worth of Rs. 1600, not on the Rs. 1760 face value - using the face value gives about 9 months, which is why that option is listed.
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