Discussion
The simple interest on a certain sum for a given time and rate is ₹60, and the true discount on the same sum for the same time and rate is ₹50. What is the sum?
Answer: D
Correct answer: ₹300
The simple interest here is calculated on the face value, so it is the banker’s discount, and the standard relation applies: \[ A = \frac{\text{SI} \times \text{TD}}{\text{SI} - \text{TD}} = \frac{60 \times 50}{60 - 50} = \frac{3000}{10} = 300. \] The derivation is worth seeing. SI is interest on \( A \); TD is interest on \( A - \text{TD} \). Since interest is proportional to principal at a fixed rate and time, \[ \frac{\text{SI}}{\text{TD}} = \frac{A}{A - \text{TD}}, \] and cross-multiplying gives the formula. Checking: the present worth is \( 300 - 50 = 250 \), and \( 50/250 = 60/300 = 0.2 \), so both are computed at \( RT = 20 \). The difference \( \text{SI} - \text{TD} = 10 \) is the banker’s gain, and it is also the interest on the true discount: \( 50 \times 0.2 = 10 \).
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