$A$ and $B$ can complete a piece of work in $45$ and $40$ days respectively. Both started to work together,but after some days $A$ left and $B$ alone completed the remaining work in $23$ days. For how many days did $A$ work?

$A$ and $B$ can do a piece of work in $30$ and $36$ days respectively. They began the work together,but $A$ leaves after some days and $B$ finished the remaining work in $25$ days. After how many days did $A$ leave?

If $A, B,$ and $C$ can complete a work in $6$ days together. If $A$ can work twice as fast as $B$ and thrice as fast as $C$,then the number of days $C$ alone can complete the work is (in days):

If $x$ men can do a piece of work in $x$ days,then the number of days in which $y$ men can do the same work is (in days)

$A, B$ and $C$ can complete a work in $2 \, h$. If $A$ does the job alone in $6 \, h$ and $B$ in $5 \, h$,how long will it take for $C$ to finish the job alone? (in $h$)

$A$ daily wage earner gets a daily wage at the rate of $Rs. 150$ per day,subject to the condition that he will have to pay a penalty at the rate of $Rs. 25$ per day for the days he is absent. At the end of $60$ days,he receives an amount of $Rs. 7,600$. The number of days he worked is: