A sum of Rs. 1,550 is lent partly at 5% per annum and partly at 8% per annum, both on simple interest. The total interest received after 3 years is Rs. 300. What is the ratio of the amount lent at 5% to the amount lent at 8%?

Introduction / Context:
This question involves splitting a total sum into two parts, each invested at a different simple interest rate. The total interest over a fixed time is known, and we are asked to find the ratio in which the original principal is divided between the two rates. Such questions are standard in aptitude tests and reinforce algebraic thinking with simple interest concepts.

Given Data / Assumptions:

• Total principal = Rs. 1,550
• Part of the amount is lent at 5% per annum
• The remaining amount is lent at 8% per annum
• Time = 3 years
• Total simple interest over 3 years = Rs. 300

Concept / Approach:
Let the amount lent at 5% be x rupees, so the amount lent at 8% is 1550 - x rupees. We compute the interest for each part using the simple interest formula and add them to match the given total interest. This will give us an equation in x, from which we can find both parts and then their ratio.

Step-by-Step Solution:
Let amount at 5% = xAmount at 8% = 1550 - xInterest from x at 5% for 3 years = (x * 5 * 3) / 100 = 15x / 100Interest from (1550 - x) at 8% for 3 years = ((1550 - x) * 8 * 3) / 100 = 24(1550 - x) / 100Total interest = 300, so:15x / 100 + 24(1550 - x) / 100 = 300Multiply both sides by 100: 15x + 24(1550 - x) = 3000015x + 37200 - 24x = 3000037200 - 9x = 300009x = 7200, so x = 800Amount at 5% = Rs. 800 and at 8% = 1550 - 800 = Rs. 750Required ratio = 800 : 750 = 16 : 15
Verification / Alternative check:
We can verify by recomputing the interest. Interest on Rs. 800 at 5% for 3 years is (800 * 5 * 3) / 100 = Rs. 120. Interest on Rs. 750 at 8% for 3 years is (750 * 8 * 3) / 100 = Rs. 180. Total interest = 120 + 180 = Rs. 300, which matches the given information, so the ratio is correct.

Why Other Options Are Wrong:
The ratios 5:8, 6:7 and 17:18 do not satisfy the total interest condition of Rs. 300 when we back calculate the interest. They either give a total lower or higher than 300, so they cannot be correct.

Common Pitfalls:
Common errors include mixing up the parts, using 3 years incorrectly, or forgetting to multiply the interest by time for both portions. Some candidates also forget to convert the final ratio into simplest form. Always reduce ratios to their lowest terms before choosing the answer.

Final Answer:
The ratio of the amount lent at 5% to the amount lent at 8% is 16:15.