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.


4. If the perimeter of a triangle is 45 cm and its sides are in the ratio 2: 3: 4, find the sides of the triangle.

Solution:

Perimeter of the triangle = 45 cm

Ratio of the sides of the triangle = 2 : 3 : 4

Sum of ratio terms = (2 + 3 + 4) = 9

The sides of the triangle \(\frac{2}{9}\) × 45 cm, \(\frac{3}{9}\) × 45 cm and \(\frac{4}{9}\) × 45 cm,

i.е., 10 cm, 15 cm and 20 cm. 

Hence, the sides of the triangle are 10 cm, 15 cm and 20 cm.

You might like these

● 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.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Money | Conversion of Money from Rupees to Paisa

    Dec 03, 24 01:29 AM

    Worksheet on Money
    Practice the questions given in the worksheet on money. This sheet provides different types of questions where students need to express the amount of money in short form and long form

    Read More

  2. 2nd Grade Money Worksheet | Conversion of Money | Word Problems

    Dec 03, 24 01:19 AM

    Match the following Money
    In 2nd grade money worksheet we will solve the problems on writing amount in words and figures, conversion of money and word problems on money. 1. Write T for true and F for false. (i) Rs. is written…

    Read More

  3. Subtraction of Money | Subtraction with Conversion, without Conversion

    Dec 02, 24 01:47 PM

    Subtraction of Money
    In subtraction of money we will learn how to subtract the amounts of money involving rupees and paise to find the difference. We carryout subtraction with money the same way as in decimal numbers. Whi…

    Read More

  4. Word Problems on Addition of Money |Money Word Problems|Money Addition

    Dec 02, 24 01:26 PM

    Word Problems on Addition of Money
    Let us consider some of the word problems on addition of money. We have solved the problems in both the methods i.e., with conversion into paise and without conversion into paise. Worked-out examples

    Read More

  5. Addition of Money | Add The Amounts of Money Involving Rupees & Paisa

    Nov 29, 24 01:26 AM

    3rd Grade Addition of Money
    In addition of money we will learn how to add the amounts of money involving rupees and paisa together. We carryout with money the same way as in decimal numbers. While adding we need to follow that t…

    Read More