Direct and Inverse Proportions

If $x$ and $y$ are in direct proportion, and the value of $x$ is doubled, what happens to the value of $y$?

A $100$ gram serving of a snack contains $12$ grams of fat. How many grams of fat are in a $250$ gram pack of the same snack?

If $\frac{x}{y} = \frac{9}{4}$ and $y = 16$, what is the value of $x$?

A water faucet fills a $20 \text{ L}$ bucket in $4$ minutes. How much time will it take to fill a $50 \text{ L}$ bucket?

An elevator ascends $120\text{ floors}$ in $15\text{ minutes}$. How many floors will it ascend in $25\text{ minutes}$ at the same speed?

If $3.5\text{ kg}$ of apples cost ₹$420$, what is the cost of $5.5\text{ kg}$ of apples?

A certain machine makes $150\text{ plastic bottles}$ in $40\text{ minutes}$. How many bottles can it make in $2\text{ hours}$?

If $x$ and $y$ are in a direct proportion such that $x = 2.4$ when $y = 1.8$, determine the value of $y$ when $x$ is increased to $6.4$.

A weaver uses $1.5 \text{ kg}$ of wool to make $3$ handmade sweaters. At this rate, how many kilograms of wool will be needed to produce $10$ sweaters?

A stack of $450$ identical paper sheets has a thickness of $4.5 \text{ cm}$. How many sheets of the same paper would be required to create a stack with a thickness of $12.6 \text{ cm}$?

2 men build a fence in 6 days. How many days will 3 men take to build the same fence?

16 workers can complete a project in 10 days. How many days will 20 workers take to complete it?

A car travels at 50 km/h for 2 hours to cover a distance. What speed must it maintain to cover the same distance in 1 hour?

If $x$ varies inversely as $y$ and $x = 4$ when $y = 9$, find $x$ when $y = 6$.

A person takes 2500 steps to cover a distance where each step is $70$ cm long. What will be his step length if he covers the same distance in 2800 steps?

12 workers can complete a task in 15 days. If the number of workers is reduced to 10, how many days will they take to complete the same task?

10 harvesting machines take 6 days to clear a field. If the job must be done in 5 days, how many machines are required?

If 30 men can reap a field in 15 days, how many days will 20 men take to reap the same field?

If 76 men can complete a job in 42 days, in how many days can 56 men complete the same job?

100 men can build a bridge in 120 days. How many more men are needed to complete the bridge in 100 days?

If $12$ men can complete a piece of work in $20$ days, how many days will $15$ men take to do the same work?

If $x$ and $y$ are in direct proportion and $x = 6$ when $y = 10$, find $y$ when $x = 15$.

If $10$ toys cost ₹$450$, how much will $15$ toys cost?

$5$ persons can build a wall in $48 \text{ hours}$. How many persons are required to do the same work in $30 \text{ hours}$?

A construction contractor has enough food for $40$ laborers to last for $18\text{ days}$. After $3\text{ days}$, $10$ more laborers join the site. How many more days will the remaining food last?

An airplane flies $2,400\text{ km}$ in $3\text{ hours}$. How far will it fly in $7\text{ hours}$ assuming it maintains the same average speed?

A rectangular garden has a length of $24\text{ m}$ and a width of $15\text{ m}$. If the width is changed to $10\text{ m}$ but the area remains the same, what is the new length of the garden?

$20$ men can build a $100\text{ m}$ long wall in $10$ days. How many days will $25$ men take to build a $150\text{ m}$ long wall of the same type?

A family of $4$ has food provisions for $30$ days. If $2$ guests join the family and the daily food consumption per person is reduced to $80\%$ of the original amount, how long will the provisions last?

The cost of painting a square-shaped wall with a side of $10\text{ m}$ is $₹2500$. What will be the cost of painting a similar square wall with a side of $15\text{ m}$ at the same rate per square unit?