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John is only 40% as efficient as Jesse. If John alone can do a piece of work in 35 days, how many days will it take the duo to complete the work, if t
Question

John is only 40% as efficient as Jesse. If John alone can do a piece of work in 35 days, how many days will it take the duo to complete the work, if they work together?

A.

9 days

B.

11 days

C.

12 days

D.

10 days

Correct option is D

Given:
John's efficiency is 40% of Jesse's efficiency.
John alone can complete the work in 35 days.
Concept Used:
Efficiency is inversely proportional to the time taken to complete the work.
Solution:
Let Jesse's efficiency be E . Then, John's efficiency is 0.4E .
Let the total work be W .

John’s work rate=W35 per day\text{John's work rate} = \frac{W}{35} \, \text{per day}​​

Jesse’s work rate=W35×10.4=W14 per day\text{Jesse's work rate} = \frac{W}{35} \times \frac{1}{0.4} = \frac{W}{14} \, \text{per day}

Combined work rate=W35+W14=2W+5W70=7W70=W10 per day\text{Combined work rate} = \frac{W}{35} + \frac{W}{14} = \frac{2W + 5W}{70} = \frac{7W}{70} = \frac{W}{10} \, \text{per day}
Time=WCombined work rate=WW10=10 days\text{Time} = \frac{W}{\text{Combined work rate}} = \frac{W}{\frac{W}{10}} = 10 \, \text{days}  

Alternative Method:
 John's efficiency is 40% of Jesse's efficiency.   

John=Jesse×40100John = Jesse \times \frac{40}{100}  

JohnJesse=25\frac{John}{Jesse} = \frac{2}{5} 

Total work = 2×35=70 unit2 \times 35 = 70 \ unit  

The complete the whole work  together = 702+5=10\frac{70}{ 2 + 5 } = 10​​

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