We know the formula for calculating Simple Interest. SI = (P × r × t)/100 Where, SI = Simple Interest P = Principle r = Rate of interest (in percentage) t = Time period From the question, Rate of interests at which sums was lent are r1 = 6%, r2 = 5% Amount recovered in each case, A = Rs. 2300 Let, Sums lent be P each. Time period for sum at 6% = t years Time period for sum at 5% = (t + 1/2) years (∵ 1 year = 12 months) So, P + (P × 6 × t)/100 = 2300 ⇒ 100P + 6Pt = 230000 …(1) Also, P + /100 = 2300 ⇒ 100P + 5Pt + (5/2)P = 230000 …(2) From (1) and (2), 100P + 6Pt = 100P + 5Pt + (5/2)P ⇒ t = (5/2) years From (1), 100P + 6P × (5/2) = 230000 ⇒ 115P = 230000 ⇒ P = Rs. 2000 ∴ The sums lent were Rs. 2000 each for 6% and 5% for 2.5 years and 3 years respectively.