Question
A team of workers can finish a task in 36 days. However, 5
workers leave the task every day, and it gets done in 48 days. Find the time needed for 90 workers to complete the task working together.Solution
ATQ,
Let the number of workers be 'W' and each has efficiency 'e' units/day.
Total work = W × 36 × e = 36We units.
ATQ:
36We = W × e + (W - 5 × 1) × e + (W - 5 × 2) × e + .... + (W - 5 × 47) × e
Or,
36W = 48W - 5 × (1 + 2 + 3 + .... + 47)
⇒ 12W = 5 × 47 × (48/2)
⇒ W = (5 × 47 × 24) ÷ 12 = 470
Let the required time be T days for 90 workers.
So, 36 × 470 × e = 90 × T × e
⇒ T = (36 × 470) ÷ 90 = 188
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