WBCS Mains 2019 Official Paper-VI

$12$ men can do a piece of work in $30$ days. How many extra men should be engaged to do the work in $20$ days?

A man and a boy can do a piece of work in $36$ days. If the man works alone for the last $10$ days, the work is completed in $40$ days. How long would the boy take to do it alone?

$A$ and $B$ together can do a piece of work in $25$ days. If $B$ works alone for the last $10$ days, it is completed in $30$ days. In how many days can $A$ alone do it?

$1200$ boys and $600$ girls are examined in a test. $42\%$ of the boys and $30\%$ of the girls passed. Find the percentage of those who failed.

If $50$ men do a piece of work in $12$ days working $8\text{hours}$ a day, how many hours a day would $60$ men have to work in order to do another piece of work twice as great in $16$ days?