Chain Rule

$40$ persons take $6 \mathrm{days}$ to complete a certain task working $10 \mathrm{hours}$ a day. How many hours a day will be sufficient for $30$ persons to complete the same task in $10 \mathrm{days}?$

A steel plant got an order of $1000$ pieces of steel coil. $250$ pieces of steel coil are produced by employing $1000$ persons, working $15 \mathrm{hours} \mathrm{per} \mathrm{day}$ in $100 \mathrm{days}$. During the quality check, it was advised that the working hours must be reduced by $5 \mathrm{hours}$, then find the additional number of persons required to complete the project in $200 \mathrm{days}$.

In a road construction project, $72$ men can complete the work in $500 \mathrm{days}$. Now, all $72$ men worked for first $450 \mathrm{days}$. As the lock-down is imposed due to COVID-19 for $10 \mathrm{days}$. Find the number of extra men required to complete the work before $10 \mathrm{days}$ than expected.
 

In a construction site, $2500$ men can complete the work in $90 \mathrm{days}$, and after working for $30 \mathrm{days}$, $2375$ existing men left the work and $500$ newbies join the team. In how many days the remaining work will be completed?

In a construction project, $N$ men can complete the work in $T \mathrm{days}$, and after they had worked for $t \mathrm{days}$. The same number of men join the workforce. In how many days the remaining work will be completed? 

In a power plant, $300$ pumps are employed for working $10$ hours a day that can fill the boilers in $2$ days. How many hours a day the $400$ pumps are required to fill the boiler in a single day?

The fourth proportional to $0.05,0.45.16$ is:

If $27$ men can do a piece of work in $30$ days. In what time $135$ men can do another piece of work $3$ times as greater?

If $56$ men can type a book in $10$ days. How many more men are needed so that the book can be completed in $8$ days?

$48$ boys can do a work in $72$ days. After $24$ days, some boys came and the remaining work is finished in $24$ days. Find the extra number of boys.

$36$ men can do a work in $48$ days. After $12$ days, some men left the work and the remaining work is finished in $48$ days. How many men left the work?

In a hotel, there was enough food for consumption by $12$ men for $30$ days. After $10$ days, $3$ men came in hotel. For how many days the food will last for them?

In a military base, they had food for consumption by $36$ soldiers for $20$ days. After $5$ days, $6$ soldiers left. How many days the remaining food will last for them?

A wall $60m\times 30m\times 20 m$ can be built by $3$ men in $4$ days working $6$hrs/day. How many men are needed to construct a wall  $20 m\times 40 m\times 10 m$ in $4$  days working $2$ hr/day?

If 4 men or 8 women can do a piece of work in 15 days, in how many days can 6 men and 12 women do the same piece of work?

Some persons can do a piece of work in $12$ days. Two times the number of such persons will do half of the work in :

Two cogged wheels, of which one has $16$ cogs and the other has $27$ work into each other if the latter turns $80$ times in three quarters of a minute, how often does the other turn in $8 \mathrm{seconds}?$

If a piece of work could be completed in $24$ days by $98$ men, how many men would it take to complete it in $21$ days?

$4$mat-weavers can weave $4$mats in $4$days. At the same rate, how many mats would be woven by $8$mat-weavers in $8$days?

An industrial loom weaves $0.128$metres of cloth every second. Approximately, how many seconds will it take for the loom to weave $25$metres of cloth?