Ratio and Proportion

What is the ratio of $400\text{ g}$ to $1\text{ kg}$ in its simplest form?

Simplify the ratio $6:15$.

Simplify the ratio $12:60$.

In a group of $30$ people, $10$ prefer tea. What is the ratio of people who prefer tea to those who do not?

Simplify the ratio $120 : 180 : 300$.

A bag contains $24$ marbles: $8$ are red and the rest are blue. What is the ratio of red marbles to blue marbles in simplest form?

Express the ratio of $48$ minutes to $1.2$ hours in simplest form.

In $18$-karat gold, the ratio of gold to other metals is $18$ to $6$. What is this ratio in simplest form?

Simplify the ratio $1.2 : 2 \frac{2}{5}$.

If $a:b = 2:3$ and $c:b = 5:6$, find the ratio $a:c$.

Share $\$1000$ in the ratio $2:3$. How much is the smaller share?

Divide $49$ items in the ratio $2:5$. What is the number of items in the smaller share?

Share $22$ beads in the ratio $1:1$. How many beads does each person get?

Divide $\$36$ in the ratio $5:4$. What is the value of the larger share?

When $£100$ is shared among three people in the ratio $2:3:5$, what is the difference between the largest and the smallest share?

A wire $88$ m long is cut in the ratio $5:6$. What is the length of the smaller piece?

A lottery win of $£450$ is split in the ratio $2:7$. How much is the larger share?

A line segment $AB$ is 40 cm long. A point $C$ is placed on the segment such that it divides $AB$ in the ratio $3:5$. What is the length of the shorter segment $AC$?

The ratio of boys to girls in a youth club is $8:5$. After 6 girls leave the club, the ratio of boys to girls becomes $2:1$. How many boys are in the club?

A pole is painted Red, White, and Blue in the ratio $2:5:3$ by length. If the Red section is $1.2$ meters long, what is the total length of the pole?

If $10$ pencils cost $\$4$, what is the cost of $25$ pencils at the same unit price?

If $3$ bars of soap cost $\$2.70$, what is the cost of $8$ bars of the same soap?

A set of $2$ emergency candles burns for a total of $10$ hours if used one after the other. How many candles are needed to provide $30$ hours of light?

A store sells $3$ pairs of socks for $\$15$. How much would $10$ pairs of socks cost?

A pool is being filled with water at a rate of $150$ liters every $5$ minutes. How many liters of water will be in the pool after $12$ minutes?

A $100$g serving of yogurt contains $80$ calories. How many calories are in a $250$g tub of the same yogurt?

A person takes $1500$ steps to walk $1.2$ km. How many steps would they take to walk $5$ km at the same stride length?

An express train travels a distance of $165$ km in $1$ hour and $50$ minutes. What is the average speed of the train in km/h?

To make $500$ ml of a specific soup, $120$ g of onions are needed. How many kilograms of onions are required to make $12.5$ liters of this soup?

The ratio of red to blue to yellow pens in a box is $2:3:5$. If there are $30$ blue pens, how many yellow pens are in the box?