Simple Interest — ₹ 1550 is lent partly at 5% and partly at 8% per annum (simple). Over 4 years, the total interest received is ₹ 400. Find the ratio of the amounts lent at 5% to 8%.

Introduction / Context:
Splitting a principal into two parts at different simple interest rates over the same time yields a linear equation in the split amounts. The ratio follows directly from that equation.

Given Data / Assumptions:

• Total principal = ₹ 1550, time = 4 years.
• Part at 5% = x; part at 8% = 1550 − x.
• Total SI in 4 years = ₹ 400.

Concept / Approach:
Total SI = 4 * (0.05x + 0.08(1550 − x)) = 400. Solve for x and express the split as a ratio.

Step-by-Step Solution:
0.20x + 0.32(1550 − x) = 400.0.20x + 496 − 0.32x = 400 ⇒ −0.12x = −96 ⇒ x = 800.Thus amounts: at 5% = 800, at 8% = 750 ⇒ ratio = 800 : 750 = 16 : 15.

Verification / Alternative check:
Interest: 800*0.05*4 = 160; 750*0.08*4 = 240; total = 400 as given.

Why Other Options Are Wrong:
Other ratios do not reproduce the total ₹ 400 interest.

Common Pitfalls:
Forgetting to multiply by time (4 years) or mishandling the algebraic signs.

Final Answer:
16 : 15