HOW TO SOLVE RATIO WORD PROBLEMS

In this section, you will learn how word problems on ratio can be solved.

Let us look at the stuff which are required to solve word problems on ratio. 

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 is

= '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 is 

=  11x / 15   (see stuff 2)

After increment in wages in the ratio

22 : 25

Wages per worker is 

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

That is, 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

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