Direct Proportion

When $x$ and $y$ are in direct proportion and if $y$ is doubled, then what happens to $x$?

In a camp there are$420 \mathrm{kg}$ of rice sufficient for $98$persons for $45$ days. The number of days that $60 \mathrm{kg}$ of rice will last for $42$ persons is 

A car covers a distance of $765 \mathrm{km}$ in $51$ litres of petrol. How much distance would it cover in $30$ litres of petrol?( in $\mathrm{km}$).

The weight of an iron pipe varies directly with its length. If $8$ feet of an iron pipe weighs $3.2 \mathrm{kg}$ find the proportionality constant $k$ and determine the weight of a $36$ feet iron pipe.

Ashwani has a road map with a scale of $1 \mathrm{cm}=24 \mathrm{km}$

Which mathematical concept is used here? Why we use road map?

Ashwani has a road map with a scale of $1 \mathrm{cm}=24 \mathrm{km}$

If the distance on the road is $k \mathrm{km}$, if corresponding distance covered on map is $11 \mathrm{cm}$. Find the value of $k$.

Ashwani has a road map with a scale of $1 \mathrm{cm}=24 \mathrm{km}$. The distance covered in the map is $k \mathrm{cm}$, if she drives on a road for $168 \mathrm{km}$, then find the value of $k.$

The students of Anju's class sold posters to raise money. Anju wanted to apply the concept of variation for finding the amount of money her class would make for different numbers of posters sold. She knew that they could raise $₹250$ for every $60$ posters sold.

If Anju's class raise exactly $₹2000$, then how many posters would they need to sell?

The students of Anju's class sold posters to raise money. Anju wanted to apply the concept of variation for finding the amount of money her class would make for different numbers of posters sold. She knew that they could raise $₹250$ for every $60$ posters sold.

How much money would Anju's class make for selling $102$ posters? Express your answer in $₹$)

It is given that $l$ varies directly as $m$. Find $m$, when $l$ is $8$ using the constant of proportion, $k=\frac{1}{3}$.

It is given that $l$ varies directly as $m$.

Find $l$, when $m$ is $33$ (Use constant of proportion, $k=\frac{1}{3}$).

It is given that $l$ varies directly as $m$. Find the constant of proportion in fraction $k$, when $l$ is $6$ and $m$ is $18$.

It is given that $l$ varies directly as $m$

Write an equation which relates $l$ and $m$

A volleyball court is in a rectangular shape and its dimensions are directly proportional to the dimensions of the swimming pool given below. Find the width of the pool.

A water tank casts a shadow $21 \mathrm{m}$ long. A tree of height $9.5 \mathrm{m}$ casts a shadow $8 \mathrm{m}$ long at the same time. The lengths of the shadows are directly proportional to their heights. Find the height of the tank.

Here is a keyboard of a harmonium.

Why do we use musical instruments in daily life? What is the value depicted from it?

Here is a keyboard of a harmonium.

This pattern of keys is repeated on larger keyboard. How many black keys would you expect to find on a keyboard with $14$such patterns?

Fill in the blanks in the following table by a suitable number, if $x$ and $y$ vary directly.

A recipe for a particular type of muffins requires $1$ cup of milk and $1.5$ cups of chocolate. Riya has $7.5$ cups of chocolate. If she is using the recipe as a guide, how many cups of milk will she need to prepare muffins?

The mass of an aluminium rod varies directly with its length. If a $16 \mathrm{cm}$ long rod has a mass of $192 \mathrm{g}$, then find the length of the rod whose mass is $105 \mathrm{g}$.