Question : A work can be completed by N men in 15 days. 5 men leave the work after 3 days. The remaining work was completed in 18 days. What is the value of N?
Option 1: 18
Option 2: 21
Option 3: 15
Option 4: 12
Correct Answer: 15
Solution :
Let the efficiency of one man be E
Total work done by N men for 15 days with efficiency of E = N × E × 15 = 15NE
Total work done by N men in 3 days = 3NE
The remaining work = 15NE – 3NE = 12NE
After 3 days 5 men left the work. Remaining workers = (N – 5)
The remaining work is completed in 18 days by (N – 5) workers,
⇒ 18 × (N – 5) × E = 12NE
⇒ 18(N – 5) = 12N
⇒ 18N – 90 = 12N
⇒ 6N = 90
⇒ N = 15
Hence, the correct answer is 15.
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