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
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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