Question

Had been one man less, then the number of days required to do a piece of work would have been one more. If the number of Man Days required to complete the work is 56, how many workers were there?

• A. 14
• B. 9
• C. 6
• D. 8

Answer 1

Answer:

D. 8

Solution:

Given:

Number of man days required to complete the work = 56

Calculation:

Let the number of man be "m" and number of days be "d"

Number of man days = m × d = 56

Number of man = (m – 1)

⇒ Number of days = (d + 1)

⇒ Number of man days = (m – 1) (d + 1)

⇒ md =(m – 1) (d + 1)

⇒ md = md – d + m – 1

⇒ m – d = 1

putting d = 56/m 

⇒ m – 56/m = 1 

⇒ m² – 56 = m

⇒ m² – m – 56 = 0

⇒ m² – 8m + 7m – 56 = 0

⇒ m(m – 8) + 7(m – 8) = 0

⇒ (m – 8) (m + 7) = 0 

⇒ m = 8, – 7 

m is number of man, so m cannot be negative 

⇒ m = 8 

∴ The Number of workers is 8.