Question : A group of men decided to do a job in 11 days but 16 men left the work after each day. The work, as a result, was completed in 15 days. How many men were there initially in the group?
Option 1: 400
Option 2: 480
Option 3: 420
Option 4: 450
Correct Answer: 420
Solution :
Given: A group of men decided to do a job in 11 days but 16 men left the work after each day.
Total time taken to complete the work = 15 days
Let there be $x$ number of men in the group with efficiency of 1 unit per day.
Time required to complete all the work if x men were working = 11 days
So, total work = 11$x$ units
According to the question,
$x + (x-16) + (x-16×2) + (x-16×3)+ .......... + (x-16×14) = 11x$
⇒ $15x -16 (1+2+ ......... + 14) = 11x$
⇒ $4x = 16×\frac{(14)(15)}{2}$
⇒ $x = 420$
Hence, the correct answer is 420.
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