Question : A work can be completed by 20 men in 50 days. 30 more men join them after 10 days of work. How many days will be saved in the completion of the work?
Option 1: 18 days
Option 2: 20 days
Option 3: 24 days
Option 4: 28 days
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Correct Answer: 24 days
Solution : 20 men can finish a work = 50 days Let the number of days taken after the increment of 30 people be $x$. According to the question, Total work = Efficiency × Time = 50 × 20 M1 × D1 = M2 × D2 ⇒ 20 × 50 = 20 × 10 + 50 × $x$ ⇒ 50 × $x$ = 800 ⇒ $x$ = 16 Total time taken = 10 + 16 = 26 days $\therefore$ Number of days saved = 50 – 26 = 24 days Hence, the correct answer is 24 days.
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