Ratio and Proportion

Simplify the ratio $17 : 51$.

Express the ratio of $4$ minutes to $40$ seconds in its simplest form.

Find the simplest form of the ratio $13 : 39$.

What is the ratio of $3$ items to $1$ score? (Note: $1$ score = $20$ items)

Find the ratio of the number of consonants in the word 'APPLE' to the number of consonants in the word 'BANANA'.

If $\frac{1}{x} : \frac{1}{y} = 4 : 5$, find the ratio $x : y$.

If $x : y = 5 : 4$, find the value of $(2x + 3y) : (3x - 2y)$.

If $4A = 5B = 2C$, find the ratio $A : B : C$.

The sum of three numbers is 98. If the ratio of the first to the second is $2 : 3$ and that of the second to the third is $5 : 8$, then the second number is:

If $x : y = 2 : 1$, find the value of $(x^2 - y^2) : (x^2 + y^2)$.

If $2$ kg of apples cost $₹160$, find the cost of $5$ kg of apples using proportion.

Find the value of $x$ in $x : 1.1 = 10 : 1$.

Check if the numbers $2, 5, 6, 15$ are in proportion.

Find $x$ if $40 : 60 = 2 : x$.

If $x : 1.2 = 5 : 2$, find the value of $x$.

If the numbers $10, 20, x,$ and $60$ are in proportion, find the value of $x$.

The ratio of the perimeters of two squares is $3 : 5$. If the perimeter of the smaller square is $24$ cm, what is the perimeter of the larger square?

If the triplicate ratio of $x : y$ is $8 : 27$, find the value of $(x^2 + y^2) : xy$.

If $\frac{A}{2} = \frac{B}{5} = \frac{C}{8}$, find the value of $\frac{A - B + C}{B}$.

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

If $3$ sets of guitar strings cost $₹900$, find the cost of $2$ such sets.

A pedometer shows that a person takes $3,000$ steps in $30\text{ minutes}$. How many steps does the person take in $1\text{ minute}$?

If $7\text{ kg}$ of dog food lasts for $7\text{ days}$, how many kilograms are needed for $10\text{ days}$?

If $5$ boxes hold $500$ paper clips in total, how many paper clips are there in $1$ box?

A subscription for $4\text{ months}$ costs $₹ 1,400$. What is the cost for a full year ($12\text{ months}$) at the same rate?

If a $20\text{ m}$ long wire weighs $1.5\text{ kg}$, what is the weight of $50\text{ m}$ of the same wire?

A garrison of $300\text{ men}$ has provisions for $45\text{ days}$. If $200\text{ more men}$ join the garrison, how many days will the provisions last?

If $45$ men can do a work in $20$ days, how many days will $15$ men take to do $3/4$ of the same work?

A typist can type $100$ pages of $30$ lines each, with $10$ words in each line, in $20$ hours. How many hours will he take to type $120$ pages of $25$ lines each, with $12$ words in each line?

If $12$ cows eat as much as $15$ buffaloes, and $20$ buffaloes can graze a field in $12$ days, how many days will $16$ cows take to graze the same field?

If the ratio of boys to girls in a class is $5:3$ and there are $24$ girls, find the number of boys.

Find the mean proportional between $4$ and $16$.

The speed of a cycle is $15$ km/h and the speed of a scooter is $45$ km/h. Find the ratio of their speeds.

If $3$ bags of rice weigh $150$ kg, find the weight of $5$ such bags.

The length and breadth of a rectangle are in the ratio $7:4$. If the perimeter is $220$ m, find the length of the rectangle.

A car travels at a speed of $45$ km/h and covers a distance in $3.2$ hours. To cover the same distance in $2.4$ hours, what should be its speed?

$15$ postcards cost ₹$22.50$. How much will $36$ postcards cost?

The ratio of the number of sides of two regular polygons is $1:2$, and the ratio of their interior angles is $3:4$. Find the number of sides of the first polygon.

A contractor estimated that it would take $12$ men $20$ days to build a wall. If he wants the wall built in $15$ days, how many more men should he hire?

If $a/b = c/d$, then $(a+c)/(b+d)$ is equal to: