Question : A can complete a piece of work alone in 120 days, while A and B, working together, can complete the same work in 72 days. In how many days can B, working alone, complete this piece of work?
Option 1: 180
Option 2: 200
Option 3: 160
Option 4: 216
Correct Answer: 180
Solution :
One day's work of A = $\frac{1}{120}$
One day's work of A and B together = $\frac{1}{72}$
Let B alone complete the work in b days.
One day's work of B = $\frac{1}{b}$
$\frac{1}{120}+\frac{1}{b}=\frac{1}{72}$
⇒ $\frac{1}{b}=\frac{1}{72} -\frac{1}{120}$
⇒ $\frac{1}{b}=\frac{15-9}{1080}$
⇒ $\frac{1}{b}=\frac{1}{180}$
⇒ $\therefore b=180$ days
Hence, the correct answer is 180.
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