Question : George can do 35% of the total work in 6 days, Jim and George together completed a piece of work in 12 days. In how many days could Jim, working alone, complete the entire task?
Option 1: 36
Option 2: 40
Option 3: 42
Option 4: 45
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Correct Answer: 40
Solution :
Given, 35% of the total work is done by George in 6 days.
Jim and George can do a piece of work in 12 days.
Let us assume Jim can do a task in $x$ days.
⇒ Jim's one day work = $\frac{1}{x}$ part of the work
And George's $\frac{35}{100}$ of the work is done in 6 days
⇒ George can do a piece of work in $\frac{6\times 100}{35}=\frac{120}{7}$ days
⇒ George's one day work = $\frac{7}{120}$
Jim and George can do a piece of work in 12 days
Jim and George's one day work = $\frac{1}{12}$
According to the question,
$\frac{1}{x}+\frac{7}{120}=\frac{1}{12}$
⇒ $\frac{120+7x}{120x}=\frac{1}{12}$
⇒ $120 + 7x=\frac{120x}{12}$
⇒ $120+7x = 10x$
⇒ $120=3x$
⇒ $x=40$ days
Hence, the correct answer is 40.
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