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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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