Splitting ₹ 5000 between 3% and 8% simple interest: A person invests a total of ₹ 5000, part at 3% p.a. and the remainder at 8% p.a. simple interest. If the total interest in 3 years is ₹ 750, find the amounts invested at each rate.

Introduction / Context:
We distribute a fixed principal between two simple-interest rates. Using total interest over a known time period allows solving for the split uniquely by linear equations.

Given Data / Assumptions:

• Total principal = ₹ 5000.
• Time = 3 years.
• Rates: 3% p.a. and 8% p.a.
• Total interest (3 years) = ₹ 750.

Concept / Approach:
Let x be the amount at 3% and (5000 − x) at 8%. Total interest = 3-year interest at 3% plus 3-year interest at 8%. Solve the resulting linear equation for x and then compute the remainder.

Step-by-Step Solution:
Interest = x*0.03*3 + (5000 − x)*0.08*3.= 0.09x + 0.24(5000 − x) = 0.09x + 1200 − 0.24x.Total = 1200 − 0.15x = 750 ⇒ 0.15x = 450 ⇒ x = ₹ 3000.Remainder = ₹ 2000 at 8%.

Verification / Alternative check:
3-year interest: 3000*0.03*3 = 270; 2000*0.08*3 = 480; total = 750, which matches the given.

Why Other Options Are Wrong:

• Equal split (₹ 2500 each) gives a different total interest.
• The other pairs do not satisfy the equation 1200 − 0.15x = 750.

Common Pitfalls:

• Forgetting to multiply by 3 years at both rates.

Final Answer:
Rs. 3000 and Rs. 2000