Worksheet on Dividing a Quantity in a Given Ratio Concept provides problems on quantities into two parts and three parts of a given ratio. We will discuss the quantities of a given ratio in various aspects to get a clear understanding of the whole concept to the children. As we know, a ratio is a comparison of quantities of the same unit and it can be described as a fraction. Here, the ratio of X and Y is defined as X : Y = \(\frac{X}{Y}\). The quantity X in the ratio is called antecedent and Y is the consequent.

Practice the questions given in the below Dividing quantity in a given Ratios worksheet pdf and answer all complex calculations with ease. Dividing quantities in a given ratio worksheet makes you learn the concept in a fun-learning & engaging manner. This Math Dividing a Quantity in a Given Ratio Word Problems Worksheet gives a step-to-step explanation so that you don’t feel bored and difficult to study & solve the calculations.

Also Check:

## Dividing a Quantity in a Given Ratio Worksheet | Sharing Ratios Worksheet with Answers

**Example 1:**

A number is divided into two parts in the ratio of 4: 9. If the larger part is 270, then find the actual number and the smaller part.

**Solution:**

The given ratio is 4: 9.

Let the numbers be 4k and 9k

Given larger part of the number is 270.

Now, we find the number by solving 9k = 270.

k = \(\frac{270}{9}\)

⇒ k = 30

Another number is 4k, substitute the k value in 4k.

4k = 4 × 30 = 120.

Thus, the smaller part number is **120** and the actual number is **390**.

**Example 2:**

A bag contains 3 dollars, 50 cents, 4 dollars in the ratio of 5: 4: 2. The total amount is $ 2450. Find the number of each denomination?

**Solution:**

Let the number of each denomination be 5x, 4x, and 2x respectively.

The amount of 3 dollars = 5x × 300 cents = 1500x cents

The amount of 50 cents = 4x × 50 cents = 200x cents

The amount of 4 dollars = 2x × 400 cents = 800x cents

The total amount given = 2450 × 100 cents =245000 cents.

Now, 1500x + 200x + 800x = 245000

⇒ 2500x = 245000

⇒ x = \(\frac{245000}{2500}\)

⇒ x = 98

Now, we substitute the x value in each denomination.

The number of 3 dollars i.e., 5x = 5×98 = 490

The number of 50cents i.e., 4x = 4×98 = 392

The number of 4 dollars i.e., 2x = 2×98 = 196

Therefore, the denominations of each number are **490, 392, **and** 196**.

**Example** **3:**

The sum of the numbers is 250, and the two numbers are in the ratio 4: 6. Find the numbers?

**Solution:**

Given two numbers in the ratio is 4: 6.

Let the two numbers be 4a and 6a.

Now, 4a+ 6a = 250

⇒ 10a = 250

⇒ a = \(\frac{250}{10}\)

⇒ a = 25

Next, we multiply the value of ‘a’ with the two numbers.

4a = 4×25 = 100

6a = 6×25 = 150

Thus, the numbers are **100 **and** 150**.

**Example 4:**

Divide 420 into three parts which are in the ratio 3: 6: 5.

**Solution:**

The given number is 420 and the ratio is 3: 6: 5.

Now, to calculate the sum of the ratios = 3+6+5 = 14

Next, divide the three parts

First part = \(\frac{3}{14}\)×420 = 3×30 = 90

Second part = \(\frac{6}{14}\)×420 = 6×30 = 180

Third part = \(\frac{5}{14}\)×420 = 5×30 = 150

Hence, 420 can be divided into **90**,** 180**, and **150** in the ratio of 3: 6: 5.

Get to know the different topics pertaining to the 10th Grade Math all in one place and stand out from the rest of the crowd.

**Example 5:**

Four workers worked for 7 hours, 6 hours, 5 hours, and 6 hours. The total wage of ₹14640 was divided among the four workers according to their number of hours worked. How much did they get for the hours they worked?

**Solution:**

Let the hours of the workers worked to be in the ratio of 7: 6: 5: 6.

The sum of the ratio = 7+6+5+6 = 24hours

Now, get the amount per hour = Total wage / Hours worked = ₹14640/24 = ₹610 per hour

The wage of the first worker = 7×₹610 = ₹4270

The wage of the second worker = 6×₹610 = ₹3660

The wage of the third worker = 5×₹610 = ₹3050

The wage of the fourth worker = 6×₹610 = ₹3660

Therefore, each worker got the amount of **₹4270**, **₹3660**, **₹3050**, and **₹3660**.

**Example 6:**

Divide 4m 25cm in the ratio 4: 6.

**Solution:**

Given quantity 4m 25cm

Now, first, we have to convert the given quantity into one unit.

As we know, 1m = 100cm

4m = 4×100 = 400cm

4m 25cm = 400cm + 25cm = 425cm.

Given ratio is 4: 6

The total number of parts = 4x+6x = 10x

Now, 10x = 425

⇒ x = \(\frac{425}{10}\) = 42.5

So,

The quantity of first number 4x = 4×42.5 = 170cm

The quantity of second number 6x = 6×42.5 = 255cm

Hence, the two quantities of the two numbers are **170cm** and **255cm**.

**Example 7:**

The length and breadth of a rectangle are in the ratio of 8: 5. If the breadth is 85cm, then find the length of a rectangle?

**Solution:**

Given the ratio of length and the breadth is 8: 5 and the breadth is 85cm

Let the length be 8k and breadth be 5k.

Now, breadth 5k = 85cm

⇒ k = \(\frac{85}{5}\) = 17cm

Here, length = 8k

⇒ 8k = 8×17 = 136cm

Thus, the length of a rectangle is **136cm**.

**Example 8:**

A certain sum of money is divided into three parts in the ratio 4: 3: 2. If the first part is ₹448, then find the total amount, the second part, and the third part?

**Solution:**

Given three parts ratio is 4: 3: 2.

Let the amount of money be 4x, 3x, and 2x.

From the given the first part is ₹448.

4x = ₹448

⇒ x = \(\frac{448}{4}\) = 112

Thus, x = 112

Now,

3x = 3×112 = 336 and 2x = 2×112 = 224

Therefore, the second amount = ₹336

the third amount = ₹224

The total amount of money = First amount + Second amount + Third amount = ₹448 + ₹336 + ₹224 = ₹1008.

Hence, the total amount of money is **₹1008**, the second part is **₹336**, and the third part is **₹224**.