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 total time elapsed on the faulty clock. The clock is set right at 9 a.m. on the first day. The faulty clock shows 2 p.m. on the following day. The time elapsed from 9 a.m. on day 1 to 9 a.m. on day 2 is 24 hours. The time elapsed from 9 a.m. on day 2 to 2 p.m. on day 2 is 2 p.m. - 9 a.m. = 5 hours. The total time elapsed on the faulty clock is 24 hours + 5 hours = 29 hours. Step 2: Determine the gain rate of the faulty clock. The clock gains 10 minutes in 24 hours. This means that for every 24 hours of correct time, the faulty clock shows 24 hours + 10 minutes. Convert 10 minutes to hours: 10 min = (10)/(60) hours = (1)/(6) hours. So, when the correct clock shows 24 hours, the faulty clock shows 24 + (1)/(6) = (144+1)/(6) = (145)/(6) hours. Step 3: Calculate the actual time passed on the correct clock. Let T_F be the time shown by the faulty clock and T_C be the time shown by the correct clock. The ratio of faulty time to correct time is constant: T_F (faulty time)Correct time = (145)/(6) hours24 hours = (145)/(6 × 24) = (145)/(144) We know that the faulty clock has shown T_F = 29 hours. We need to find the corresponding correct time T_C. (29)/(T_C) = (145)/(144) To solve for T_C: T_C = 29 × (144)/(145) Since 145 = 5 × 29, we can simplify: T_C = 29 × (144)/(5 × 29) T_C = (144)/(5) hours Step 4: Convert the correct time elapsed into hours and minutes. T_C = (144)/(5) hours = 28 (4)/(5) hours Convert the fractional part to minutes: (4)/(5) hours = (4)/(5) × 60 minutes = 4 × 12 minutes = 48 minutes So, the correct time elapsed is 28 hours and 48 minutes. Step 5: Calculate the correct time. The clock was set right at 9 a.m. on day 1. Add 28 hours and 48 minutes to 9 a.m. (day 1): 9 a.m. (day 1) + 24 hours = 9 a.m. (day 2) 9 a.m. (day 2) + 4 hours = 1 p.m. (day 2) So, 9 a.m. (day 1) + 28 hours = 1 p.m. (day 2). Now add the remaining 48 minutes: 1 p.m. (day 2) + 48 minutes = 1:48 p.m. (day 2). The correct time is 1:48 p.m. on the following day. This corresponds to option (C). The final answer is C) 48 min past 1 / 1 ਵਜੇ ਕੇ 48 ਮਿੰਟ. Last free one today — make it count tomorrow, or type /upgrade for unlimited.