Find the present worth of Rs 930 due 3 years hence at 8 percent per annum simple interest. Also determine the amount of discount allowed on this bill.

Introduction / Context:
This true discount question asks for both the present worth and the discount on a bill due after several years when money is valued using simple interest. The present worth is the amount that, if invested now at the given rate, will grow to the future amount. The discount is the difference between the future amount and its present worth. Such questions help in understanding the basic idea of present value and discounting.

Given Data / Assumptions:
- Future amount due (face value of the bill) = Rs 930.
- Time until due = 3 years.
- Rate of simple interest = 8 percent per annum.
- We need to compute the present worth and then the discount.
- The options given refer to the discount amount only.

Concept / Approach:
Under simple interest, amount A after time t years from present value P is A = P * (1 + r * t / 100), where r is the annual rate. Rearranging, the present value is P = A / (1 + r * t / 100). The true discount is TD = A − P. We will first compute the present value using the formula and then find the discount by subtraction.

Step-by-Step Solution:
Step 1: Amount due A = Rs 930. Step 2: Rate r = 8 percent per annum, time t = 3 years. Step 3: Compute the factor 1 + r * t / 100 = 1 + 8 * 3 / 100 = 1 + 24 / 100 = 1.24. Step 4: Present worth P = A / 1.24 = 930 / 1.24. Step 5: Calculate 930 / 1.24 = 750 rupees. Step 6: True discount TD = A − P = 930 − 750 = Rs 180. Step 7: So, present worth is Rs 750 and the discount allowed is Rs 180.

Verification / Alternative check:
Check that investing Rs 750 at 8 percent simple interest for 3 years reaches the amount due. Interest for 3 years = 750 * 8 * 3 / 100 = 750 * 24 / 100 = 180. Amount after 3 years = principal + interest = 750 + 180 = 930, which matches the bill amount. Therefore, the discount and the present worth values are consistent.

Why Other Options Are Wrong:
Options 186, 185 and 189 all represent different discount amounts. If we subtract these from 930, the resulting present values do not grow to exactly 930 in 3 years at 8 percent simple interest. Only a discount of Rs 180 gives a present value which compounds correctly to the face value.

Common Pitfalls:
A frequent mistake is to calculate simple interest on the face value directly and treat that as the discount. However, the discount is the interest on the present value, not on the amount due. Another error is to use the wrong time or to mix up r * t / 100 with r / (100 * t). Always compute the factor 1 + r * t / 100 and divide the future amount by this factor to get the present worth.

Final Answer:
The discount is Rs 180 and the present worth is Rs 750.