Dividing a Quantity into Three Parts in a Given Ratio

We will discuss here how to solve different types of word problems on dividing a quantity into three parts in a given ratio.

1. Divide $ 5405 among three children in the ratio 112 : 2 : 115.

Solution:

Given ratio = 112 : 2 : 115

                = 32 : 2 : 65

Now multiply each term by the L.C.M. of the denominators

                 = 32 × 10 : 2 × 10 : 65 × 10, [Since, L.C.M. of 2 and 5 = 10]

                 = 15 : 20 : 12

So, the amount received by three children are 15x, 20x and 12x.

15x + 20x + 12x = 5405

              ⟹ 47x = 5405

                 ⟹ x = 540547

      Therefore, x = 115

Now,

15x = 15 × 115 = $ 1725

20x = 20 × 115 = $ 2300

12x = 12 × 115 = $ 1380

Therefore, amount received by three children are $ 1725, $ 2300 and $ 1380.


2. A certain sum of money is divided into three parts in the ratio 2 : 5 : 7. If the third part is $224, find the total amount, the first part and second part.

Solution:

Let the amounts be 2x, 5x and 7x

According to the problem,

        7x = 224

      ⟹ x = 2247

Hence, x = 32

Therefore, 2x = 2 × 32 = 64 and 5x = 5 × 32 =160.

So, the first amount = $ 64 and the second amount = $ 160

Hence, total amount = First amount + Second amount + Third amount

                             = $ 64 + $ 160 + $ 224

                             = $ 448


3.  A bag contains $ 60 of which some are 50 cent coins, some are $ 1 coins and the rest are $ 2 coins. The ratio of the number of respective coins is 8 : 6 : 5. Find the total number of coins in the bag.

Solution:

Let the number of coins be a, b and c respectively.

Then, a : b : c is equal to 8 : 6 : 5

Therefore,  a = 8x, b = 6x, c = 5x 

Therefore, the total sum = 8x × 50 cent + 6x × $ 1 + 5x × $ 2

                                  = $ (8x × 12 + 6x ×  1 + 5x ×  2)

                                  = $ (4x + 6x + 10x)

                                  = $ 20x

Therefore, according to the problem,

$ 20x = $ 60

  ⟹ x = $60$20

  ⟹ x = 3

Now, the number of 50 cent coins = 8x = 8 × 3 = 24

The number of $ 1 coins = 6x = 6 × 3 = 18

The number of $ 2 coins = 5x = 5 × 3 = 15

Therefore, the total number of coins =  24 + 18 + 15 = 57.



4. A bag contains $ 2, $ 5 and 50 cent coins in the ratio 8 : 7 : 9. The total amount is $ 555. Find the number of each denomination.

Solution:

Let the number of each denomination be 8x , 7x and 9x respectively.

The amount of $ 2 coins = 8x × 200 cents = 1600x cents

The amount of $ 5 coins = 7x × 500 cents = 3500x cents

The amount of 50 cent coins = 9x × 50 cents = 450x cents

The total amount given = 555 × 100 cents = 55500 cents

Therefore, 1600x + 3500x + 450x = 55500

                                  ⟹ 5550x = 55500

                                         ⟹ x = 555005550

                                         ⟹ x = 10

Therefore, the number of $ 2 coins = 8 × 10 = 80

The number of $ 5 coins = 7 × 10 = 70

The number of 50 cent coins = 9 × 10 = 90


● Ratio and proportion






10th Grade Math

From Dividing a Quantity 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. Successor and Predecessor | Successor of a Whole Number | Predecessor

    Jul 29, 25 12:59 AM

    Successor and Predecessor
    The number that comes just before a number is called the predecessor. So, the predecessor of a given number is 1 less than the given number. Successor of a given number is 1 more than the given number…

    Read More

  2. Worksheet on Area, Perimeter and Volume | Square, Rectangle, Cube,Cubo

    Jul 28, 25 01:52 PM

    Volume of a Cuboids
    In this worksheet on area perimeter and volume you will get different types of questions on find the perimeter of a rectangle, find the perimeter of a square, find the area of a rectangle, find the ar…

    Read More

  3. Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox

    Jul 25, 25 03:15 AM

    Volume of a Cube and Cuboid
    We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks:

    Read More

  4. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

    Jul 24, 25 03:46 PM

    Volume of Cuboid
    Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

    Read More

  5. Volume of a Cube | How to Calculate the Volume of a Cube? | Examples

    Jul 23, 25 11:37 AM

    Volume of a Cube
    A cube is a solid box whose every surface is a square of same area. Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure i…

    Read More