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A man can do a work in 10 days. The man along with a boy can do the same work in 8 days. What is the ratio of efficiencies of work of the man and the boy?

  1. 2 : 1
  2. 3 : 1
  3. 4 : 1
  4. 5 : 1

Answer (Detailed Solution Below)

Option 3 : 4 : 1

Detailed Solution

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Given:

Man's work days = 10 days

Man + Boy's work days = 8 days

Formula used:

Efficiency = Total work / Time

Calculations:

LCM(10, 8) = 40 (Total work)

Man's efficiency = 40 / 10 = 4 units/day

Man + Boy's efficiency = 40 / 8 = 5 units/day

Boy's efficiency = (Man + Boy)'s efficiency - Man's efficiency

⇒ Boy's efficiency = 5 - 4 = 1 unit/day

Ratio of efficiencies (Man : Boy) = 4 : 1

∴ The ratio of efficiencies of the man and the boy is 4 : 1.

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