Question
A certain number of students can complete the assignment
together in 12 days. All of them started the assignment together, but 20 students left the assignment every day, so the assignment was completed in 16 days instead. Find the time it would take for 120 students to complete the same assignment.Solution
ATQ, Let the number of students be 'S' and efficiency of each student be 'e' units/day. Total assignment = S × 12 × e = '12Se' units ATQ, 12Se = S × e + (S - 20 × 1) × e + (S - 20 × 2) × e + (S - 20 × 3) × e + .... + (S - 20 × 15) × e Or, 12S = 16S - 20 × (1 + 2 + 3 + .... + 15) Or, 4S = 20 × 15 × (16/2) [since, sum of first 'n' natural numbers = (n/2) × (n + 1) ] So, 'S' = 600 Let the required time taken by 120 students be 't' days. So, 12 × 600 × e = 120 × t × e Or, 't' = (7,200/120) = 60
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