Discussion
The banker’s discount on a sum due 1 year 8 months hence is \( \frac{11}{10} \) of the true discount. What is the rate per cent per annum?
Answer: D
Correct answer: 6%
The ratio of the two discounts depends only on \( RT \): \[ \frac{\text{BD}}{\text{TD}} = \frac{100 + RT}{100}. \] Setting this equal to \( \frac{11}{10} \), \[ \frac{100 + RT}{100} = \frac{11}{10} \;\Rightarrow\; 100 + RT = 110 \;\Rightarrow\; RT = 10. \] The time is 1 year 8 months, that is \( T = \frac{5}{3} \) years, so \[ R = \frac{10}{5/3} = 10 \times \frac{3}{5} = 6. \] The rate is 6% per annum. The useful point is that the ratio of BD to TD never involves the face value at all - it is fixed entirely by the rate and the time. That is why a problem giving only a ratio is nonetheless solvable, and why the sum due is not needed here.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development