Divide a Number into Three Parts in a Given Ratio

To divide a number into three parts in a given ratio

Let the number be p. It is to be divided into three parts in the ratio a : b : c.

Let the parts be x, y and z. Then, x + y + z = p .................... (i)

and        x = ak, y =bk, z = ck.................... (ii)

Substituting in (i), ak + bk + ck = p

  ⟹ k(a + b + c) = p

Therefore, k = \(\frac{p}{a + b + c}\)

Therefore, x = ak = \(\frac{ap}{a+ b + c}\), y = bk = \(\frac{bp}{a+ b + c}\), z = ck = \(\frac{cp}{a+ b + c}\).

The three parts of p in the ratio a : b : c are

\(\frac{ap}{a+ b + c}\), \(\frac{bp}{a+ b + c}\), \(\frac{cp}{a+ b + c}\).



Solved examples on dividing a number into three parts in a given ratio:

1. Divide 297 into three parts that are in the ratio 5 : 13 : 15

Solution:

The three parts are \(\frac{5}{5 + 13 + 15}\) ∙ 297, \(\frac{13}{5 + 13 + 15}\) ∙ 297 and \(\frac{15}{5 + 13 + 15}\) ∙ 297

 i.e., \(\frac{5}{33}\) ∙ 297, \(\frac{13}{33}\) ∙ 297 and \(\frac{15}{33}\) ∙ 297 i.e., 45, 117 and 135.

 

2. Divide 432 into three parts that are in the ratio 1 : 2 : 3

Solution:

The three parts are \(\frac{1}{1 + 2 + 3}\) ∙ 432, \(\frac{2}{1 + 2 + 3}\) ∙ 432 and \(\frac{3}{1 + 2 + 3}\) ∙ 432

i.e., \(\frac{1}{6}\) ∙ 432, \(\frac{2}{6}\) ∙ 432 and \(\frac{3}{6}\) ∙ 432

i.e., 72, 144 and 216.

 

3. Divide 80 into three parts that are in the ratio 1 : 3 : 4.

Solution:

The three parts are \(\frac{1}{1 + 3 + 4}\) ∙ 80, \(\frac{3}{1 + 3 + 4}\) ∙ 80 and \(\frac{4}{1 + 3 + 4}\) ∙ 80

i.e., \(\frac{1}{8}\) ∙ 80, \(\frac{3}{8}\) ∙ 80 and \(\frac{4}{8}\) ∙ 80

i.e., 10, 30 and 40.


● Ratio and proportion




10th Grade Math

From Divide a Number into Three Parts in a Given Ratio to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Fundamental Geometrical Concepts | Point | Line | Properties of Lines

    Apr 18, 24 02:58 AM

    Point P
    The fundamental geometrical concepts depend on three basic concepts — point, line and plane. The terms cannot be precisely defined. However, the meanings of these terms are explained through examples.

    Read More

  2. What is a Polygon? | Simple Closed Curve | Triangle | Quadrilateral

    Apr 18, 24 02:15 AM

    What is a polygon? A simple closed curve made of three or more line-segments is called a polygon. A polygon has at least three line-segments.

    Read More

  3. Simple Closed Curves | Types of Closed Curves | Collection of Curves

    Apr 18, 24 01:36 AM

    Closed Curves Examples
    In simple closed curves the shapes are closed by line-segments or by a curved line. Triangle, quadrilateral, circle, etc., are examples of closed curves.

    Read More

  4. Tangrams Math | Traditional Chinese Geometrical Puzzle | Triangles

    Apr 18, 24 12:31 AM

    Tangrams
    Tangram is a traditional Chinese geometrical puzzle with 7 pieces (1 parallelogram, 1 square and 5 triangles) that can be arranged to match any particular design. In the given figure, it consists of o…

    Read More

  5. Time Duration |How to Calculate the Time Duration (in Hours & Minutes)

    Apr 17, 24 01:32 PM

    Duration of Time
    We will learn how to calculate the time duration in minutes and in hours. Time Duration (in minutes) Ron and Clara play badminton every evening. Yesterday, their game started at 5 : 15 p.m.

    Read More