Proportional Reasoning-1

If $x$ and $y$ vary inversely, and $x_1 = 2, y_1 = 12$, find $y_2$ if $x_2 = 4$.

If $x$ and $y$ vary directly, and $x_1 = 3, y_1 = 6$, find $y_2$ if $x_2 = 5$.

A car travels $150$ km in $3$ hours. What is the distance covered by the car in $1$ hour at the same speed?

If $10$ pens cost $₹ 150$, how many pens can be bought for $₹ 75$?

A gear with $24$ teeth is meshed with a smaller gear having $16$ teeth. If the larger gear makes $40$ revolutions per minute, how many revolutions per minute does the smaller gear make?

A garrison of 500 men had provisions for 24 days. A reinforcement of 300 men arrives. For how many days will the provisions last now?

25 meters of a specific wire weighs 1000 grams. What is the weight of 15 meters of the same wire?

A bottle of $500$ ml juice costs Rs $45$. A $2$-liter pack of the same juice costs Rs $162$. What is the percentage saving when buying the $2$-liter pack compared to four $500$ ml bottles?

If $x$ and $y$ are in inverse proportion such that $x_1 = 8$ and $y_1 = 10$. If $x_2 = 5$, find $y_2$.

If $15$ men can complete a work in $40$ days. After $10$ days, $5$ men left. How many more days will the remaining men take to finish the work?

What is the ratio of even numbers to odd numbers among the integers from $1$ to $10$ (inclusive)?

Which of the following is equivalent to the ratio $2:9$?

Find the ratio of $200$ g to $1$ kg.

If $\frac{x}{6} = \frac{5}{3}$, find the value of $x$.

The ratio of the diagonal of a square to its side is:

If $x : y = 5 : 8$, find the value of $(4x - 2y) : (x + y)$.

The ratio of oxygen to nitrogen in the air is approximately $1 : 4$. If a room contains $2500 \text{ cubic meters}$ of air, how many cubic meters of oxygen are there?

The speeds of three cars are in the ratio $2 : 3 : 4$. Find the ratio of the time taken by these cars to travel the same distance.

If $x : y = 3 : 2$, find the value of $(x^3 - y^3) : (x^3 + y^3)$.

A certain sum of money is distributed among $A, B$, and $C$ in the ratio $2 : 3 : 4$. If $B$'s share is ₹150 less than $C$'s share, what is the total sum distributed?

Simplify the ratio $150:450$.

Find the ratio of $12$ hours to $1$ day in simplest form.

Express $14:21$ in its simplest form.

What is the ratio of $8$ kg to $400$ g in simplest form?

Express the ratio of $50$ minutes to $2$ hours in its simplest form.

Simplify the triple ratio $0.9 : 2.7 : 4.5$ to its lowest terms.

What is the ratio of $800$ m to $4.8$ km in its simplest form?

What is the simplest form of the ratio $\sqrt{3} : \sqrt{27}$?

Find the simplest ratio of the reciprocal of $\frac{2}{3}$ to the reciprocal of $\frac{3}{4}$.

If $x$ is $20\%$ more than $y$, find the simplest ratio $x:y$.

A worker is paid ₹$1500$ for $5\text{ days}$ of work. If his total wages during a month are ₹$9000$, for how many days did he work?

If $3$ kg of apples cost ₹$450$, how many kg of apples can be bought for ₹$750$?

If $x/y = 5/2$ and $x=25$, what is the value of $y$?

A batch of bottles is packed in $25$ boxes with $12$ bottles in each box. If the same batch is packed using $20$ bottles in each box, how many boxes would be filled?

A book consists of $250$ pages, with each page containing $36$ lines of text. If the book is re-formatted to have $45$ lines on each page while keeping the same total amount of text, how many pages will the new version have?

A textile mill uses $15$ identical machines that consume a total of $1200$ units of electricity per day. If $5$ of these machines are shut down for maintenance, how many units of electricity will the mill consume in a day using only the remaining machines?

If $x$ and $y$ are in direct proportion and $\frac{x_1}{y_1} = \frac{x_2}{y_2}$, then if $x_1=5, y_1=20, y_2=52$, find $x_2$.

A farmer has enough food to feed $20$ animals in his cattle for $6$ days. How long would the food last if there were $10$ more animals in his cattle?

If $x$ and $y$ are in inverse proportion and $x_1 = 8, y_1 = 15$. Find $y_2$ if $x_2 = 10$.

Two variables $x$ and $y$ are such that $xy = k$. If $x$ is reduced by $50\%$, find the new value of $y$ in terms of the original $y$.

Divide $64$ in the ratio $3:5$. What is the larger share?

If a quantity of $35$ is divided in the ratio $2:5$, what are the two values?

What is the ratio of $5$ kg to $500$ g in its simplest form?

Divide $100$ in the ratio $7:3$. What is the smaller part?

Three friends $A, B,$ and $C$ share a packet of $480$ candies in the ratio $\frac{1}{3} : \frac{1}{4} : \frac{1}{6}$. How many candies does $A$ receive?

The ratio of the prices of two shirts is $7:9$. If the price of the first shirt is increased by $10\%$ and the second by $₹140$, the new ratio becomes $11:15$. Find the original price of the first shirt.

The ratio of the number of men to women in a committee of $45$ is $2:3$. If $5$ more women join the committee, what will be the new ratio of men to women?

In a mixture of 60 liters, the ratio of milk and water is $2 : 1$. If the ratio of the milk and water is to be $1 : 2$, then the amount of water to be further added must be:

A sum of money is to be distributed among A, B, C, D in the proportion of $5 : 2 : 4 : 3$. If C gets ₹ 1,000 more than D, what is B's share?

Ratio of the earnings of A and B is $4 : 7$. If the earnings of A increase by $50\%$ and those of B decrease by $25\%$, the new ratio of their earnings becomes $8 : 7$. What are A's earnings?

Convert $250 \text{ mm}$ into centimeters.

How many grams are in $3$ tonnes? ($1 \text{ tonne} = 1,000 \text{ kg}$)

Ratio of $5 \text{ days}$ to $100 \text{ hours}$ is:

Convert $0.1 \text{ Litre}$ to milliliters.

An chemical reaction produces gas at a rate of $7.2\text{ kg}$ per hour. Express this production rate in grams per second ($\text{g/s}$).

If a copper wire $5\text{ m}$ long has a mass of $2\text{ kg}$, what is the mass of $150\text{ cm}$ of the same wire?

Convert $3.6\text{ km/h}$ into $\text{cm/s}$.

Express the ratio of $0.04\text{ km}$ to $25\text{ decameters (dam)}$ in its simplest form.

A specific type of metal sheet has a mass of $3.2\text{ kg}$ per square meter. What is the total mass of a rectangular sheet measuring $250\text{ cm}$ by $80\text{ cm}$?

An athlete runs $1.5\text{ km}$ in exactly $5\text{ minutes}$. What is the athlete's average speed in meters per second ($\text{m/s}$)?