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A person plans to pay off a debt of Rs 3600 in 40 annual installments forming an Arithmetic Progression. After 30 installments, one-third of the debt remains unpaid. Find the first installment value.
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Solution: Step 1: Total debt = Rs 3600 Step 2: After 30 installments, 2/3 of debt paid = 2 * 1200 = 2400 Step 3: Let first installment = a, common difference = d Step 4: Using sum formula for 30 terms: 2400 = 15 * (2a + 29d) Step 5: Simplify: 160 = 2a + 29d Step 6: For 40 terms: 3600 = 20 * (2a + 39d) Step 7: Simplify: 180 = 2a + 39d Step 8: Solve equations: d = 2, a = 51
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