Question : A group of men decided to do a job in 6 days, but 18 men dropped out every day. If the job was completed in 8 days, then how many men initially decided to do the job?
Option 1: 300
Option 2: 252
Option 3: 188
Option 4: 150
Correct Answer: 252
Solution :
Total work = Efficiency of each worker × Number of days to finish × Number of total workers
Let there be Q men initially with the efficiency of 1 unit per day.
Total work = Q × 1 × 6 = 6Q units
According to the question,
Q + (Q - 18) + (Q - 18 × 2) + .... + (Q - 18 × 7) = 6Q
⇒ 8Q - 18 (1 + 2 + .... + 7) = 6Q
⇒ 2Q = 18 × $\frac{7\times 8}{2}$
⇒ 2Q = 504
⇒ Q = 252
∴ There were 252 men initially.
Hence, the correct answer is 252.
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