Three men,four women and six children can complete a work in $7$ days. $A$ woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in $7$ days?

Amit and Sujit together can complete a data entry assignment in $5$ days. Sujit's speed is $80\%$ of Amit's speed and the total key depressions in the assignment are $5,76,000$. What is Amit's speed in key depressions per hour if they work for $8$ hours a day?

$2$ 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?

$P$ and $Q$ complete a certain work in $30 \, days$,$Q$ and $R$ in $40 \, days$,while $R$ and $P$ in $60 \, days$. How long will they take to finish it together? (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)

$A$ does $\frac{4}{5}$ of a work in $20 \, \text{days}$. He then calls in $B$ and they together finish the remaining work in $3 \, \text{days}$. How long would $B$ alone take to do the whole work? (in $\text{days}$)