Question

A and B can do a piece of work in 28 and 35 days respectively. They began to work together but A leaves after some time and B completed the remaining work in 17 days. After how many days did A leave ? 

(a) \(14\frac{2}{5}\) days 

(b) 9 days 

(c) 8 days 

(d) \(7\frac{5}{9}\) days

Answer 1

(c) 8 days

Suppose A left after x days. Then,

Work of (A + B) for x days = \(\frac{X}{28}\) + \(\frac{X}{35}\)

Work of B for 17 days = \(\frac{17}{35}\)

\(\therefore\) \(\frac{X}{28}\) + \(\frac{X}{35}\) + \(\frac{17}{35}\) = 1

\(\Rightarrow\) \(\frac{5X+4X}{140}\) = 1 - \(\frac{17}{35}\) = \(\frac{18}{35}\)

\(\Rightarrow\) \(\frac{9X}{140}\) = \(\frac{18}{35}\) \(\Rightarrow\) x = \(\frac{18\times140}{35\times9}\) = 8 days