Direct Proportion

If $16$ men or $20$ women can reap a field in $7$ days, in what time can $4$ men and $9$ women reap the same field?

The duration of a train journey varies as the distance and inversely as the velocity, while the velocity varies directly as the square root of the quantity of coal used, and inversely as the number of carriages in the train. In a journey of $100 \mathrm{km}$ in one and half an hour with $9$ carriages, $400 \mathrm{kg}$ of coal is required. How much coal will be consumed in a journey of $112 \mathrm{km}$ in $105$ minutes with $15$ carriages?

Rajdhani Express without its rake can go$54 \mathrm{km}$ in an hour, and the speed is diminished by a quantity that varies as the square root of the number of wagons attached. If it is known that with $16$ wagons its speed is $30 \mathrm{km}/\mathrm{h}$, the greatest number of wagons with which the engine can just move is

The speed of the engine of Kerala Express is $48 \mathrm{km}/\mathrm{h}$ when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is $30 \mathrm{km}/\mathrm{h}$ when $9$ compartments are attached, the maxi- mum number of compartments that can be carried by the engine is

A precious stone weighing $45$ grams worth $₹20,250$ is accidentally dropped and gets broken into two pieces having weights in the ratio of$4:5$. If the price varies as the square of the weight then find the loss incurred.

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?