Question

After $A$ has finished $\frac{1}{2}$ of a piece of work in $10$ days, $B$ joins for $5$ days. Later $A$ completes the work which still remains in $4$ more days. In how many days could $B$ alone have done the complete work ?

• A. $12.22$
• B. $16.66$
• C. $18.66$
• D. $19.33$

Answer 1

Answer: (B)

$16.66$

After $A$ has finished half of a job i.e. $50\%$ of job in $10$ days.
Work rate of $A=\frac{50}{10}=5\%$ per day
Later, $A$ completes the remaining work in $4$ more days. It means $A$ has completed $20\%$ another work.
So, $B$ has done $30\%$ of work in $6$ days.
Work rate of $B$ $=\frac{30}{5}=6\%$ per day.
Thus, $B$ alone can complete whole work $=\frac{100}{6}=16.66$ days.