Five men and $2$ boys,working together,can complete four times as much work per hour as a man and a boy working together. The ratio of the work completed by a man and a boy is:

The total number of men,women,and children working in a factory is $18$. They earn $Rs. 4000$ in a day. If the sum of the wages of all men,all women,and all children is in the ratio $18: 10: 12$,and the wages of an individual man,woman,and child are in the ratio $6: 5: 3$,then how much does a woman earn in a day? (in $Rs.$)

$A$ and $B$ can complete a piece of work in $30 \text{ days}$,$B$ and $C$ in $40 \text{ days}$,while $C$ and $A$ in $60 \text{ days}$. $A, B, C$ together can complete the work in (in $\text{days}$):

$A$ and $B$ can together finish a work in $30$ days. They worked at it for $20$ days and then $B$ left. The remaining work was done by $A$ alone in $20$ more days. $A$ alone can finish the work in (in days):

$A$ can complete a piece of work in $40$ days. He starts working,but having some other engagements,he leaves after $5$ days. Thereafter,$B$ completes the remaining work in $21$ days. How many days would $A$ and $B$ take to complete this work working together?

$A$ takes $10\, \text{days}$ less than the time taken by $B$ to finish a piece of work. If both $A$ and $B$ can do it in $12\, \text{days}$, then the time taken by $B$ alone to finish the work is (in $\text{days}$)