In a class, 4/5 of the students are boys and rest are girls. If 2/5 of the boys and 1/4 of girls are absent, what part of the total number of students is present?
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Solution
Given: 4/5 of the students are boys, and the rest are girls. 2/5 of boys and 1/4 of girls are absent.
Step-by-Step Solution
Total students = N
Boys:(4/5) × N = 4N/5
Girls:(1/5) × N = N/5
Boys absent:(2/5) × (4N/5) = 8N/25
Girls absent:(1/4) × (N/5) = N/20
Boys present:(4N/5 - 8N/25 = 12N/25)
Girls present:(N/5 - N/20 = 3N/20)
Total present = (12N/25 + 3N/20)
Final Calculation
LCM of 25 and 20 is 100: (12N/25 = 48N/100), (3N/20 = 15N/100)
Total present = (48N/100 + 15N/100 = 63N/100)