$2$ men alone or $3$ women alone can complete a piece of work in $4$ days. In how many days can $1$ woman and $1$ man together complete the same piece of work?

$A$ labourer can do a job in $36 \text{ hours}$. After $9 \text{ hours}$,he takes a break. What fraction of the job is yet to be done?

$A$ alone would take $27 \, \text{days}$ more to complete the job than if both $A$ and $B$ worked together. If $B$ worked alone, he would take $3 \, \text{days}$ more to complete the job than $A$ and $B$ working together. What time would they take if both $A$ and $B$ worked together? (in $\text{days}$)

If the wages of $45$ women amount to $Rs. 46575$ in $48$ days,how many men must work for $16$ days to receive $Rs. 17250$,given that the daily wage of a man is double that of a woman?

$A$ worker can complete a piece of work in $50$ days. On the first day,he works alone. On the second day,one more person joins him,on the third day,one more person joins them,and this process continues until the work is completed. How many days are needed to complete the work?

$2$ men and $4$ boys can do a piece of work in $10$ days,while $4$ men and $5$ boys can do it in $6$ days. Men and boys are paid wages according to their output. If the daily wage of a man is $Rs. 40$,then the ratio of daily wages of a man and a boy will be