$3$ men and $2$ women can do a piece of work in $15$ days. $2$ men and $3$ women can do the same work in $18$ days. The number of days to be taken by $1$ man and $1$ woman to do the work is:

How many men will be required to plough $100 \, acres$ of land in $10 \, days$ if $10 \, men$ require $8 \, days$ to plough $20 \, acres$ of land?

$A$'s $2$ days work is equal to $B$'s $3$ days work. If $A$ can complete the work in $8$ days,then to complete the work $B$ will take (in days):

Twenty-four men can complete a work in sixteen $days$. Thirty-two women can complete the same work in twenty-four $days$. Sixteen men and sixteen women started working and worked for twelve $days$. How many more men are to be added to complete the remaining work in $2$ $days$?

$12$ men can complete a piece of work in $4$ days,while $15$ women can complete the same work in $4$ days. $6$ men start working on the job and after working for $2$ days,all of them stopped working. How many women should be put on the job to complete the remaining work,if it is to be completed in $3$ 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?