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
Here are the solutions to the problems. Q1. Find the rate of interest in P.C.P.A. by which Rs. 900 will amounts to Rs. 1089 in two years? Step 1: Identify the given values. Principal (P) = Rs. 900 Amount (A) = Rs. 1089 Time (n) = 2 years Rate of interest (R) = ? Step 2: Use the compound interest formula for amount: A = P(1 + (R)/(100))^n. Substitute the given values into the formula: 1089 = 900(1 + (R)/(100))^2 Step 3: Isolate the term with R. (1089)/(900) = (1 + (R)/(100))^2 Step 4: Simplify the fraction and take the square root of both sides. ((33)/(30))^2 = (1 + (R)/(100))^2 (33)/(30) = 1 + (R)/(100) (11)/(10) = 1 + (R)/(100) Step 5: Solve for R. (R)/(100) = (11)/(10) - 1 (R)/(100) = (11 - 10)/(10) (R)/(100) = (1)/(10) R = (100)/(10) R = 10 The rate of interest is 10% per annum. The final answer is 10\% P.C.P.A.. Q2. A washing machine was purchased for Rs. 2100. After 1 year the price were reduced by 5%. What will be price of machine after 1 year? Step 1: Identify the given values. Original Price (P_0) = Rs. 2100 Rate of reduction (r) = 5% per year Time (n) = 1 year Step 2: Calculate the reduction amount. Reduction = P_0 × (r)/(100) Reduction = 2100 × (5)/(100) Reduction = 21 × 5 Reduction = Rs. 105 Step 3: Calculate the price of the machine after 1 year. Price after 1 year = Original Price - Reduction Price after 1 year = 2100 - 105 Price after 1 year = Rs. 1995 The final answer is Rs. 1995. 4 done, 1 left today. You're making progress.