Question : A can do a piece of work in 16 days. B can do the same work in 24 days. A started the work alone. After how many days should B join him, so that the work is finished in 10 days?
Option 1: 6 days
Option 2: 2 days
Option 3: 5 days
Option 4: 1 day
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Correct Answer: 1 day
Solution : 1 day's work of A $=\frac{1}{16}$ 1 day's work of B $=\frac{1}{24}$ The work can be finished in 10 days. Let $x$ be the day/days after which B joins A. So, A works for 10 days and B for $(10-x)$ days. According to the question, $\frac{10}{16}+\frac{10-x}{24}=1$ ⇒ $30+20-2x=48$ ⇒ $x=1$ Hence, the correct answer is 1 day.
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