HOW TO SOLVE RATIO WORD PROBLEMS

About the topic "How to solve ratio word problems"

"How to solve ratio word problems ?" is a big question having had by all the students who study quantitative aptitude to get prepared for competitive exams.For some students, solving ratio word problems is never being easy and always it is a challenging one for any student. 

How to solve ratio word problems ?

The get answer  for the question "How to solve ratio word problems ? "is purely depending upon the question that we have in the topic "Ratio and Proportion". The techniques and methods we apply to solve word problems in ratio will vary from problem to problem.

The techniques and methods we apply to solve a particular word problem  will not work for another word problem in this topic.

Even though we have different techniques to solve word problems in different topics of math, let us see the stuff which we have to know to get answer for the question "How to solve ratio word problems?"

Stuff needed to solve ratio word problems

To get answer for the question "How to solve ratio word problems ? ", we have to be knowing the following stuff.

Stuff 1:

For example,

If two persons A & B are earning $400 and $ 500 respectively per week, the ratio of their earnings is 

                                      A : B = 400 : 500

When we simplify, we get   A : B = 4 : 5

From the ratio 4:5, if we want to get the earning of A and B, we have to multiply the terms of the ratio  4 & 5 by 100.

From the above point, it is very clear that if we want to get original quantity from the ratio, we have to multiply both the terms of the ratio by the same number.

In the above problem, we know that we have to multiply by 100. In case, we do not know what number to be multiplied, we have to multiply by "x" or any alphabet.

For example, the ages of two persons are in the ratio  5 : 6.

Age of the 1st person = 5x

Age of the 2nd person = 6x

(The value of "x" to be found)

Stuff 2 :

If a quantity increases or decreases in the ratio a:b,

then new quantity = "b" of the original quantity divided by "a". 

That is, new quantity = ("b" x original quantity)/a

Stuff 3 :

Increment Ratio :

In a ratio, if the second term is greater than the first term, it is called increment ratio.

Examples:  7:8 , 4:5, 1:5

Decrement Ratio:

In a ratio, if the second term is smaller than the first term, it is called decrement ratio.

Examples : 8:7, 4:3, 9:7

Stuff 4 :

How to find increment ratio :

A quantity called "A" has been increased to "3A".

Now, to find the ratio in which it has been increased, just take the coefficient of A in the changed quantity "3A". It is "3".

Now we have to write this "3" as a fraction. That is 3/1. From the fraction "3/1", we have to form a increment ratio. Because, the original quantity has been increased. 

Therefore, the increment ratio from "3/1" is 1:3.

How to find decrement ratio :

A quantity called "A" has been decreased to "0.25A".

Now, to find the ratio in which it has been decreased, just take the coefficient of A in the changed quantity "0.25A". It is "0.25".

Now we have to write this "0.25" as a fraction. That is "1/4". From the fraction "1/4", we have to form a decrement ratio. Because, the original quantity has been decreased. 

Therefore, the decrement ratio from "1/4" is  4:1

Let us see how the above explained stuff help us to solve the ratio word problem given below.

Problem:

Find in what ratio, will the total wages of the workers of a factory be increased or decreased if there be a reduction in the number of workers in the ratio 15:11 and an increment in their wages in the ratio 22:25.

Solution:

Step 1 :

Let us understand the given information. There are two information given in the question. 

1. In a factory, there is a reduction in the number of workers in the ratio 15:11.

2. There is an increment in their wages in the ratio 22:25.

Step 2 :

Target of the question: In what ratio, will the total wages of the factory be increased or decreased ?

Step 3 :

Let "x" be the original number of workers 

Let "y" be the wages per worker.

Total wages = (No. of workers) x (wages per worker)

Before the given two changes,

                                  Total wages  =  xy  or  1xy

Step 4 :

After reduction in the number of workers in the ratio 15:11,

Number of workers in the factory = 11x/15      (see stuff 2)

After increment in wages in the ratio 22:25,

Wages per worker = 25y/22   (see stuff 2)

Step 5 :

After the two changes, 

Total wages = (11x/15) x (25y/22)

Total wages = (5/6)xy = (0.833)xy

Step 6 :

Before the given two changes,

Total wages = 1xy  ---------------(1)

After the given two changes,

Total wages = (0.83)xy ---------(2)

Comparing (1) & (2), it is very clear that total wages has been decreased when the two changes are applied.

i.e.,  total wages has been decreased from  (1xy) to (0.83)xy

Step 7 :

Now, to find the ratio in which it has been decreased, just take the coefficient of "xy" in total wages after the two changes applied.

It is "0.83"

Now we have to write this "0.83" as a fraction. That is "5/6". From the fraction "5/6", we have to form a decrement ratio.

That is  "5 : 6"                  (See stuff 4)

Therefore, the total wages of the factory will be decreased in the ratio 5:6.

We hope that students have received answer for the question "How to solve ratio word problems ?" when they look at the above stuff and steps explained in the  above word problem on ratio.  

And also we hope that hereafter student will not search answer for the question "How to solve ratio word problems?"

Please click the below links to know "How to solve word problems in each of the given topics"

1. Solving Word Problems on Simple Equations

2. Solving Word Problems on Simultaneous Equations

3. Solving Word Problems on Quadratic Equations

4. Solving Word Problems on Permutations and Combinations

5. Solving Word Problems on HCF and LCM

6. Solving Word Problems on Numbers

7. Solving Word Problems on Time and Work

8. Solving Word Problems on Trains

9. Solving Word Problems on Time and Work.

10. Solving Word Problems on Ages.

11.Solving Word Problems on Ratio and Proportion

12.Solving Word Problems on Allegation and Mixtures.

13. Solving Word Problems on Percentage

14. Solving Word Problems on Profit and Loss

15. Solving Word Problems Partnership

16. Solving Word Problems on Simple Interest

17. Solving Word Problems on Compound Interest

18. Solving Word Problems on Calendar

19. Solving Word Problems on Clock

20. Solving Word Problems on Pipes and Cisterns

21. Solving Word Problems on Modular Arithmetic

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