Question
A team of 'x' boys can complete a
job in 18 days if they all work together. However, every day, 15 boys leave the team after starting the task, and it now takes 24 days to finish the work. Determine the value of '0.2x'.Solution
ATQ, Let the efficiency of each boy be 'b' units/day. Total work = x Ă— 18 Ă— b = '18xb' units ATQ: 18xb = x Ă— b + (x - 15 Ă— 1) Ă— b + (x - 15 Ă— 2) Ă— b + (x - 15 Ă— 3) Ă— b + .... + (x - 15 Ă— 23) Ă— b Or, 18x = 24x - 15 Ă— (1 + 2 + 3 + .... + 23) Or, 6x = 15 Ă— (23/2) Ă— (23 + 1) [since, sum of first 'n' natural numbers = (n/2) Ă— (n + 1) ] So, 'x' = 690 Therefore, required value = 0.2 Ă— 690 = 138
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