$A$ carpenter can build a cupboard in $48 \, \text{hours}$. After $12 \, \text{hours}$, he takes a break. What fraction of the cupboard is yet to be built?

Ajay and Sunil together can complete a piece of work in $10$ days,Sunil and Sanjay in $15$ days,and Sanjay and Ajay in $20$ days. They worked together for $6$ days,and then Ajay leaves. Sunil and Sanjay worked together for $4$ more days,and Sunil leaves. How long will Sanjay take to complete the remaining work? (in days)

If $A$ and $B$ together can complete a work in $18$ days,$A$ and $C$ together in $12$ days,and $B$ and $C$ together in $9$ days,then $B$ alone can do the work in (in days)

$A$ can complete a piece of work in $10$ days,while $B$ alone can complete it in $15$ days. They work together for $5$ days and the rest of the work is done by $C$ in $2$ days. If they receive $Rs. 450$ for the whole work,how should they divide the money? (in $Rs.$)

$A, B$ and $C$ can do a piece of work individually in $8, 12$ and $15$ days,respectively. $A$ and $B$ start working,but $A$ quits after working for $2$ days. After this,$C$ joins $B$ until the completion of the work. In how many days will the work be completed?

$A$ and $B$ can complete a piece of work in $18$ days; $B$ and $C$ in $24$ days; $C$ and $A$ in $36$ days. $A$ alone can complete the work in (in days):