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

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.

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## 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.

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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.

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