Had been one menless, then the number of days required to do a piece o

1.	Had been one menless, 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?1. 142. 93. 64. 8
Answer» Correct Answer - Option 4 : 8 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.

Had been one menless, 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?1. 142. 93. 64. 8

Answer» Correct Answer - Option 4 : 8

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.

Discussion

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