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, got completed in 15 days. How many men were there initially in the group?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 420.
Let there be x men initially to do the job.
Let the efficiency of each worker be 1 unit/day.
Total work done = Efficiency of each worker × Number of workers × Time taken
Now, total work done = 11 × 1 × x = 11x
According to the given question, 16 men left the work after each day.
⇒ x + (x - 16) + (x - 16 × 2) + (x - 16 × 3) ..... + (x - 16 × 14) = 11x
⇒ 15x - ( 16 + 32 + ..... + 224) = 11x
⇒ 4x = 16 × 105
⇒ x = 420
Hence the number of men initially were 420.