A class starts at 10:00 am and lasts till 4:00 pm.
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A class starts at 10:00 am and lasts till 4:00 pm. Five periods of equal duration are held during this interval. After every period, a rest of 12 minutes is given to the students. The exact duration of each period is:
Show answer & explanation
Total class duration is 6 hours (10 am to 4 pm) = 360 minutes. With 5 periods, there are 4 rest intervals after periods 1–4 (not after period 5). Total rest time = 4 × 12 = 48 minutes. Time for periods = 360 − 48 = 312 minutes. Duration per period = 312 ÷ 5 = 62.4 minutes. However, reconsidering: if rest is given after each period including the last, then 5 × 12 = 60 minutes rest, leaving 300 minutes for periods: 300 ÷ 5 = 60 minutes each. But the standard interpretation (rest after each period means between periods, so 4 rests) gives 54 minutes per period.
Step-by-step Derivation:
Step 1: Calculate total available time from 10:00 am to 4:00 pm.
10 am to 4 pm = 6 hours = 360 minutes
Step 2: Identify rest intervals.
With 5 periods in sequence, rest occurs after each of the first 4 periods (not after the final period).
Number of rest intervals = 4
Total rest time = 4 × 12 = 48 minutes
Step 3: Calculate time available for periods.
Time for periods = Total time − Total rest time
Time for periods = 360 − 48 = 312 minutes
Step 4: Calculate duration per period.
Duration per period = 312 ÷ 5 = 62.4 minutes
Note: This doesn't match the options exactly. Re-examining: If the problem implies 5 rest periods (after each period including conceptually at the end), then:
Total rest = 5 × 12 = 60 minutes
Time for periods = 360 − 60 = 300 minutes
Duration per period = 300 ÷ 5 = 60 minutes → Option B
However, testing Option A (54 minutes):
5 periods × 54 min = 270 minutes
Remaining time = 360 − 270 = 90 minutes
Rest intervals = 90 ÷ 12 = 7.5 (doesn't work cleanly)
Testing Option B (60 minutes):
5 periods × 60 min = 300 minutes
Remaining time = 360 − 300 = 60 minutes
Rest intervals = 60 ÷ 12 = 5 intervals ✓
The most mathematically consistent answer is B) 60 minutes with exactly 5 rest periods of 12 minutes each.