Processing math: 100%

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 = pa+b+c

Therefore, x = ak = apa+b+c, y = bk = bpa+b+c, z = ck = cpa+b+c.

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

apa+b+c, bpa+b+c, cpa+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 55+13+15 ∙ 297, 135+13+15 ∙ 297 and 155+13+15 ∙ 297

 i.e., 533 ∙ 297, 1333 ∙ 297 and 1533 ∙ 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 11+2+3 ∙ 432, 21+2+3 ∙ 432 and 31+2+3 ∙ 432

i.e., 16 ∙ 432, 26 ∙ 432 and 36 ∙ 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 11+3+4 ∙ 80, 31+3+4 ∙ 80 and 41+3+4 ∙ 80

i.e., 18 ∙ 80, 38 ∙ 80 and 48 ∙ 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 29 × 45 cm, 39 × 45 cm and 49 × 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. Divisible by 2 | Test of Divisibility by 2 |Rules of Divisibility by 2

    Mar 17, 25 04:04 PM

    Divisible by 2
    A number is divisible by 2 if the digit at unit place is either 0 or multiple of 2. So a number is divisible by 2 if digit at its units place is 0, 2, 4, 6 or 8.

    Read More

  2. Worksheet on 7 Times Table | Printable Multiplication Table | Video

    Mar 17, 25 02:41 PM

    worksheet on multiplication of 7 times table
    Printable worksheet on 7 times table can be used from everywhere. Homeschoolers can also use these multiplication table sheets to practice at home.

    Read More

  3. Worksheet on 6 Times Table | Printable Multiplication Table | Video

    Mar 16, 25 03:09 PM

    worksheet on multiplication of 6 times table
    Printable worksheet on 6 times table can be used from everywhere. Homeschoolers can also use these multiplication table sheets to practice at home.

    Read More

  4. Worksheet on 5 Times Table | Printable Multiplication Table | Video

    Mar 16, 25 01:25 PM

    worksheet on multiplication of 5 times table
    Printable worksheet on 5 times table can be used from everywhere. Homeschoolers can also use these multiplication table sheets to practice at home.

    Read More

  5. Worksheet on 3 Times Table | Printable Multiplication Table | Video

    Mar 16, 25 12:59 PM

    worksheet on multiplication of 3 times table
    Printable worksheet on 3 times table can be used from everywhere. Homeschoolers can also use these multiplication table sheets to practice at home.

    Read More