$A, B$ and $C$ completed a work costing $Rs. 1800$. $A$ worked for $6$ days,$B$ for $4$ days and $C$ for $9$ days. If their daily wages are in the ratio of $5: 6: 4$,how much amount will be received by $A$ (in $Rs.$)?

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):

$A, B$ and $C$ together can finish a piece of work in $4$ days. $A$ alone can do it in $12$ days and $B$ alone in $18$ days. How many days will be taken by $C$ to do it alone?

$A$ and $B$ can complete a piece of work in $30 \text{ days}$,$B$ and $C$ can complete the same work in $20 \text{ days}$,and $A$ and $C$ can complete it in $15 \text{ days}$. If all of them work together,the time taken to complete the work will be? (in $days$)

If $12$ men and $16$ boys can do a piece of work in $5 \, \text{days}$,and $13$ men and $24$ boys can do it in $4 \, \text{days}$,then the ratio of the daily work done by a man to that of a boy is:

Hemant decided to build a farmhouse in $40$ days. He employed $100$ men in the beginning and $100$ more after $35$ days and completed the construction in the stipulated time. If he had not employed the additional men,how many days behind schedule would it have been finished? (in days)