Subscribe to our YouTube channel for the latest videos, updates, and tips.


Proportion Problems

We will learn how to solve proportion problems. We know, the first term (1st) and the fourth term (4th) of a proportion are called extreme terms or extremes, and the second term (2nd) and the third term (3rd) are called middle terms or means.

Therefore, in a proportion, product of extremes  = product of middle terms.

Solved examples:

1. Check whether the two ratios form a proportion or not:

(i) 6 : 8 and 12 : 16;                           (ii) 24 : 28 and 36 : 48

Solution:

(i) 6 : 8 and 12 : 16

6 : 8 = 6/8 = 3/4

12 : 16 = 12/16 = 3/4

Thus, the ratios 6 : 8 and 12 : 16 are equal.

Therefore, they form a proportion.

(ii) 24 : 28 and 36 : 48

24 : 28 = 24/28 = 6/7

36 : 48 = 36/48 = 3/4

Thus, the ratios 24 : 28 and 36 : 48 are unequal.

Therefore, they do not form a proportion.


2. Fill in the box in the following so that the four numbers are in proportion.

5, 6, 20, ____

Solution:

5 : 6 = 5/6

20 : ____ = 20/____

Since the ratios form a proportion.

Therefore, 5/6 = 20/____

To get 20 in the numerator, we have to multiply 5 by 4. So, we also multiply the denominator of 5/6, i.e. 6 by 4

Thus, 5/6 = 20/6 × 4 = 20/24

Hence, the required numbers is 24


3. The first, third and fourth terms of a proportion are 12, 8 and 14 respectively.  Find the second term.

Solution:

Let the second term be x.

Therefore, 12, x, 8 and 14 are in proportion i.e., 12 : x = 8 : 14

⇒ x × 8 = 12 × 14, [Since, the product of the means = the product of the extremes]

⇒ x = (12 × 14)/8

⇒ x = 21

Therefore, the second term to the proportion is 21.

More worked-out proportion problems:

4. In a sports meet, groups of boys and girls are to be formed. Each group consists of 4 boys and 6 girls. How many boys are required, if 102 girls are available for such groupings?

Solution:

Ratio between boys and girls in a group = 4 : 6 = 4/6 = 2/3 = 2 : 3

Let the number of boys required = x

Ratio between boys and girls = x : 102

So, we have, 2 : 3 = x : 102

Now, product of extremes = 2 × 102 = 204

Product of means = 3 × x

We know that in a proportion product of extremes = product of means

i.e., 204 = 3 × x

If we multiply 3 by 68, we get 204 i.e., 3 × 68 = 204

Thus, x = 68

Hence, 68 boys are required.


5. If a : b = 4 : 5 and b : c = 6 : 7; find a : c.

Solution:

a : b = 4 : 5

⇒ a/b = 4/5

b : c = 6 : 7

⇒ b/c  = 6/7

Therefore, a/b × b/c = 4/5 × 6/7

⇒ a/c = 24/35

Therefore, a : c = 24 : 35


6. If a :  b = 4 : 5 and b : c = 6 : 7; find a : b : c.

Solution:

We know that of both the terms of a ratio are multiplied by the same number; the ratio remains the same.

So, multiply each ratio by such a number that the value of b (the common term in both the ratios) acquires the same value.

Therefore, a :  b = 4 : 5 = 24 : 30, [Multiplying both the terms by 6]

And, b : c = 6 : 7 = 30 : 35, [Multiplying both the terms by 5]

Clearly,; a : b : c = 24 : 30 : 35

Therefore, a : b : c = 24 : 30 : 35

From, the above solved proportion problems we get the clear concept how to find whether the two ratios form a proportion or not and word problems.









6th Grade Page

From Proportion Problems 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 Average | Word Problem on Average | Questions on Average

    May 17, 25 05:37 PM

    In worksheet on average interest we will solve 10 different types of question. Find the average of first 10 prime numbers. The average height of a family of five is 150 cm. If the heights of 4 family

    Read More

  2. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  3. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  4. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More

  5. Worksheet on Rounding Off Number | Rounding off Number | Nearest 10

    May 15, 25 05:12 PM

    In worksheet on rounding off number we will solve 10 different types of problems. 1. Round off to nearest 10 each of the following numbers: (a) 14 (b) 57 (c) 61 (d) 819 (e) 7729 2. Round off to

    Read More