Question : A group of men decided to do a job in 13 days but 9 men left the work after each day. The work, as a result, was completed in 16 days. How many men were initially in the group?
Option 1: 378
Option 2: 360
Option 3: 330
Option 4: 380
Correct Answer: 360
Solution :
Number of Men × Number of Days = Work Done
⇒ N
1
× D
1
= N
2
× D
2
Assume there were $x$ people in the beginning.
For LHS,
Total work = 13$x$
For RHS,
Work done on day 1 = $x$ × 1 (where 1 is 1 day)
Work done on day 2 = ($x$ – 9) ×1
Work done on day 3 = ($x$ – 18) ×1
Work done on day 16 = ($x$ – 9 × 15) × 1 = ($x$ – 135) × 1
Adding the RHS shows that the total work
$= 16x -9 \times \frac {16\times 15}{2} = 16x – 1080$
Putting LHS = RHS,
13$x$ = 16$x$ – 1080
⇒ 3$x$ = 1080
⇒ $x$ = 360
Hence, the correct answer is 360.
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