This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Calculate the principal amount (x). Kajal invested x at a compound interest rate of 5\% per annum for 2 years and 146 days. The total interest received was Rs. 9964. First, convert the time into years: 2 years and 146 days = 2 + (146)/(365) = 2 + (2)/(5) = 2.4 years. The amount A with compound interest for a fractional period is given by: A = P (1 + (R)/(100))^whole years (1 + R × fractional part of year100) Substitute P=x, R=5\%, whole years = 2, and fractional part of year = (2)/(5): A = x (1 + (5)/(100))^2 (1 + (5)/(100) × (2)/(5)) A = x ((105)/(100))^2 (1 + (1)/(20) × (2)/(5)) A = x ((21)/(20))^2 (1 + (2)/(100)) A = x ((441)/(400)) ((102)/(100)) = x ((441)/(400)) ((51)/(50)) A = x (441 × 51)/(400 × 50) = x (22491)/(20000) The compound interest (CI) is A - x: CI = x (22491)/(20000) - x = x ((22491 - 20000)/(20000)) = x ((2491)/(20000)) We are given CI = Rs. 9964: x ((2491)/(20000)) = 9964 Solve for x: x = (9964 × 20000)/(2491) Recognize that 9964 = 4 × 2491: x = 4 × 20000 = 80000 The principal amount x is Rs. 80,000. Step 2: Calculate the simple interest. Now, find the simple interest if x (Rs. 80,000) is invested at 10\% per annum for 2 years. Principal P = Rs. 80000 Rate R = 10\% Time T = 2 years The formula for simple interest (SI) is: SI = (P × R × T)/(100) SI = (80000 × 10 × 2)/(100) SI = 800 × 10 × 2 SI = 16000 The simple interest earned would be Rs. 16,000. The final answer is 16,000. That's 2 down. 3 left today — send the next one.