A can do a work in 36 days, while B can do the same work in 48 days. If A works for x days while B works for x + 2 days, then one-third of the work is completed. Find the value of x?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 6
A person who finishes a work in \(n\) days does \(\frac{1}{n}\) of it in a day, so the work done is the daily share times the number of days, and the shares of A and B are added.
A’s part in \(x\) days: \(\frac{x}{36}\); B’s part in \(x+2\) days: \(\frac{x+2}{48}\)
Together these parts make one-third of the work: \(\displaystyle\frac{x}{36}+\frac{x+2}{48}=\frac{1}{3}\)
With the LCM 144: \(4x+3(x+2)=48\), so \(7x=42\) and \(x=\) 6