Discussion

The banker's discount on a sum of money for 3/2 years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:

Answer: C

Writing \( k = \dfrac{RT}{100} \),

\[ \text{BD} = A\,k, \qquad \text{TD} = \frac{A\,k}{1+k} = \text{PW}\,k, \qquad \text{BG} = \text{BD} - \text{TD} = \text{TD}\,k \]

Write \( r \) for the annual rate as a decimal. The banker's discount for \( \tfrac{3}{2} \) years is interest on the face value:

\[ A \times r \times 1.5 = 558 \quad\Longrightarrow\quad Ar = 372 \]

The true discount for 2 years is

\[ \frac{A \times 2r}{1 + 2r} = 600 \quad\Longrightarrow\quad \frac{744}{1 + 2r} = 600 \]

\[ 744 = 600 + 1200r \quad\Longrightarrow\quad r = 0.12 = 12\% \]

Substituting \( Ar = 372 \) into the second equation is what eliminates the unknown face value.

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