# Dividing a Quantity in Three Given Ratios – Definition, Rules, Examples | How do you Divide a Quantity in Three Given Ratios?

In this platform, you will learn about the rules of dividing a quantity into three given ratios. As we know, a ratio indicates their relative sizes and always expresses the ratios in simplest form. It is a comparison of two or more different quantities having the same units of measure and it can even be denoted as a fraction.

In this dividing a quantity in three given Ratios word problems, students can get the Dividing a Quantity into Three Given Ratios Questions with Answers. In this article, you will even find the definition of dividing a quantity into three given ratios, rules, and solved example problems on dividing a quantity into three given ratios.

### Dividing a Quantity in Three Given Ratios – Definition

Dividing a quantity into three given ratios is stated as taking a common multiple that is k and then finding each part in terms of k. We have to divide a number into three parts having a ratio of 1:3:4 then, let the common multiple be k. Therefore, the three parts are 1k, 3k, and 4k. You can also download the worksheet on dividing a quantity in a given ratios pdf from this page.

### Rules for Dividing a Quantity in a Three Given Ratios

The rules of dividing a quantity into three given ratios are explained below. If a quantity K is divided into three parts in the ratio of X:Y: Z, then
(i) The first part is X/(X +Y+Z) × K.
(ii) The second part is Y/(X +Y+Z) × K, and
(iii) The third part is Z/(X+Y+Z) x K.

### Problems on Dividing a Quantity into Three Given Ratios

Problem 1: If $162 is divided among three people in the ratio of 2 : 3: 4. Find the share of each person. Solution: As given in the question, the value is$162 and the ratio is 2:3:4.
Now, we will find the share of each person.
First, find the sum of the terms of the ratio. The sum is 2 + 3 + 4 = 9.
The share of the first boy is  2/9 × 162 = $36. Next, the share of the second boy is 3/9 × 162 =$54.
The share of the third boy is 4/9 × 162= $72. Therefore, the required shares are$ 36, $54, and$72 respectively.

Problem 2: How to divide 88 into three parts in the ratio of 2:4:5. Write the divided values.

Solution:
As given in the question, the value is 88 and the ratio is 2:4:5.
Now, we need to find the sum of the given ratios.
The sum is 2+4+5 = 11.
So, the first part value is 2/11 x 88 = 16.
The second part is 4/11×88 = 32.
The third part is 5/11×88 = 40.
Hence, after dividing the values are 16, 32, and 40.

Problem 3: If the angles of a triangle are in the ratio of 2:3:4. What is the value of each angle?

Solution:
Given in the question,
Let the common ratio be 2x,3x, and 4x.
So, the common ratio is x and the angles are 2x, 3x, and 4x.
2x+3x + 4x is180 degrees.
So, 9x = 180 degrees.
X = 180/9 = 20 degrees.
The 2x angle is, 2(20) = 40 degrees.
The angle at 3x  is, 3(20) = 60 degees.
The angle at 4x is , 4(20) = 80 degrees.
Therefore, in the triangle, each angle value is 40 degrees, 60 degrees, and 80 degrees.

Problem 4: The sides of a triangle are in the ratio of 1:2:3 and the perimeter of the triangle is 36cm, find its sides?

Solution:
As given in the question, the sides are in the ratio of 1:2:3 and the perimeter is 36cm.
First, we can assume that the sides of the triangle are 1 x t, 2 x t, 3 x t = t, 2t, 3t.
The perimeter is 36cm.
So, the value is t+2t+3t = 36cm.
i . e., 6t = 36 cm
t = 36 cm/6 = 6cm.
The side of the triangle t is 6 cm.
The side of the triangle 2t is 2×6 = 12 cm.
The side of the triangle 3t is 3×6 = 18 cm.
Therefore, the sides of the triangle are 6 cm, 12 cm, and 18 cm respectively.

Problem 5: Divide Rs.1500 among A, B, and C in the ratio of 3:5:2.

Solution:
Given in the question, the value is Rs.1500 and in the ratio of 3:5:2.
Now, find the sum of the given ratios.
The sum is 3+5+2 = 10.
So, the A value is 3/10 x 1500 = Rs.450.
The B value is 5/10 x 1500 = Rs.750.
The C value is 2/10 x 1500 = Rs.300.
The total amount is First amount + Second amount + Third amount = Rs.450 + Rs.750 + Rs.300 = Rs.1500
Thus, the dividing values are  Rs.450, Rs.750, and Rs.300.

Problem 6: A bag contains 3 dollars, 50 cents, and 4 dollars in the ratio of 5: 4: 2. The total amount is \$ 2450. Find the number of each denomination?

Solution:
In the given question, the ratios are 5:4:2.
So the number for each denomination is 5x, 4x, and 2x respectively.
The amount of 3 dollars is 5x × 300 cents that is 1500x cents
The amount of 50 cents is 4x × 50 cents = 200x cents
The amount of 4 dollars is 2x × 400 cents = 800x cents
The total amount given is 2450 × 100 cents =245000 cents.
Now, 1500x + 200x + 800x = 245000
⇒ 2500x = 245000
⇒ x = 2450002500
⇒ x = 98
Now, we have to substitute the x value in each denomination. We get,
The number of 3 dollars i.e., 5x = 5×98 = 490
The number for 50cents is 4x = 4×98 = 392
The number of 4 dollars i.e., 2x = 2×98 = 196
Hence, each number denominations are 490, 392, and 196.

Problem 7: A certain sum of money is divided into three parts in the ratio of 4: 3: 2.  If the first part is ₹448, then find the total amount, the second part, and the third part respectively?

Solution:
Given that, the three parts in the ratio are 4: 3: 2.
Assume that, the amount of money is 4x, 3x, and 2x.
Using the given first part value. We will find the X value.
The first part value is ₹448.
i.e., 4x = ₹448
⇒ x = 4484 = 112
Thus, x = 112
Next, 3x = 3×112 = 336 and 2x = 2×112 = 224
Therefore, the second amount = ₹336
the third amount = ₹224
So, the total amount of money is, First amount + Second amount + Third amount
i.e., ₹448 + ₹336 + ₹224 = ₹1008.
Therefore, the total amount of money is ₹1008, ₹336, and ₹224 respectively.

### FAQs on Dividing a Quantity into Three given Ratios

1. What is meant by dividing a quantity into three given ratios?

Dividing a quantity into three given ratios is stated as taking a common multiple that is x and then finding each part in terms of x. We have to divide a number into three parts having a ratio of 1:2:4 then, let the common multiple be x. Therefore, the three parts are 1x, 2x, and 4k.

2. How many rules are there for finding the three given ratios quantity?

There are 3 rules for dividing a quantity into three given ratios.

3. How do you find the ratio of three quantities?

The following are the steps, for calculating a ratio of 3 numbers. The steps are:

• Step 1: First, find the total number of parts in the ratio by adding the numbers in the ratio together.
• Step 2: Next, find the value of each part in the ratio by dividing the given amount by the total number of parts.
• Step 3: Then, multiply the original ratio by the value of each part.

4. What happens when you divide a ratio?
When dividing ratios, we are essentially dividing a whole number into a number of smaller numbers and assigning those in proportion to the specified ratio by multiplying.

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