Two equal sums were lent on simple interest at 6% and 10% per annum respectively. The first sum was recovered two years later than the second sum and the amount in each case was Rs.1105. What was the sum (in Rs.) lent in each scheme?

Let sum be P. For second loan at 10% for t years: Amount = P(1 + 10t/100) = 1105. For first loan at 6% for (t+2) years: Amount = P(1 + 6(t+2)/100) = 1105. Equating: P(1 + 0.1t) = P(1 + 0.06t + 0.12), which gives 0.1t = 0.06t + 0.12, so 0.04t = 0.12, meaning t = 3 years. Substituting: P(1 + 0.3) = 1105, so P = 1105/1.3 = 850. The key insight is that equal amounts from different rates and times must satisfy the equation.