Aneesh borrowed some money at the rate of 5% per annum for the first 3 years, 8% per annum for the next 7 years and 12% per annum for the period beyond 10 years. If the total interest paid by him at the end of 13 years is ₹ 5,350, how much money did Aneesh borrow, if the interest is charged as simple interest?
₹ 5,000
₹ 5,500
₹ 5,100
₹ 5,800
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CBI DSP LDCE – 2023
Period 1: Rate (R1) = 5% p.a., Time (T1) = 3 years.
Simple Interest for Period 1 (SI1) = (P * R1 * T1) / 100 = (P * 5 * 3) / 100 = 15P / 100.
Period 2: Rate (R2) = 8% p.a., Time (T2) = next 7 years. Total time elapsed = 3 + 7 = 10 years.
Simple Interest for Period 2 (SI2) = (P * R2 * T2) / 100 = (P * 8 * 7) / 100 = 56P / 100.
Period 3: Rate (R3) = 12% p.a., Time (T3) = period beyond 10 years until 13 years. T3 = 13 – 10 = 3 years.
Simple Interest for Period 3 (SI3) = (P * R3 * T3) / 100 = (P * 12 * 3) / 100 = 36P / 100.
The total interest paid is the sum of simple interests for each period.
Total SI = SI1 + SI2 + SI3 = (15P / 100) + (56P / 100) + (36P / 100) = (15P + 56P + 36P) / 100 = 107P / 100.
Given that the total interest paid is ₹ 5,350.
107P / 100 = 5350.
107P = 5350 * 100.
P = (5350 * 100) / 107.
Since 5350 = 107 * 50, we have:
P = (107 * 50 * 100) / 107 = 50 * 100 = ₹ 5,000.
The amount borrowed was ₹ 5,000.