## Ratio and Proportion Word Problems — Examples & Practice - Expii

## WORD PROBLEMS ON RATIO AND PROPORTION

From the ratio 3 : 5 : 7, the ages of three boys are 3x, 5x and 7x.

Average age of three boys = 25

So, the age of the youngest boy is 15 years.

Given : Original weight of John = 56.7 kg. He is going to reduce his weight in the ratio 7:6.

We can use the following hint to find his new weight, after it is reduced in the ratio 7 : 6.

So, John's new weight is 48.6 kg.

Sum of the terms in the given ratio is

So, no. of boys in the school is

Given : Number of new girls admitted in the school is 18.

Let x be the no. of new boys admitted in the school.

After the above new admissions,

No. of boys in the school = 270 + x

No. of girls in the school = 450 + 18 = 468

Given : The ratio after the new admission is 2 : 3.

So, the number of new boys admitted in the school is 42.

From the given ratio of incomes ( 4 : 5 ),

(Expenditure = Income - Savings)

Then, expenditure of the 1st person = 4x - 50

Expenditure of the 2nd person = 5x - 50

Expenditure ratio = 7 : 9 (given)

Then, the income of the second person is

So, income of the second person is $500.

Original price of the 1st house = 16x

Original price of the 2nd house = 23x

Price of the 1st house = 16x + 10% of 16x

Price of the 2nd house = 23x + 477

After increment in prices, the ratio of prices becomes 11:20.

Then, original price of the first house is

So, original price of the first house is $848.

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Worked out Problems on Ratio and Proportion

1. Arrange the following ratios in descending order.

More solved problems on ratio and proportion are explained here with full description.

Therefore, the total amount $(60 + 90 + 150) = $300

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## Ratio and Proportion Questions & Word Problems | GMAT GRE Maths

## Introduction to Ratios

Ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

( Reference : Oxford dictionary )

Notation : Ratio of two values a and b is written as a:b or a/b or a to b.

Women : total number of people = 28 : 49 = 4 : 7

Let the number of doctors be 5x and the number of lawyers be 4x.

So the number of lawyers in the group is 4*8 = 32.

Let the number of the blocks A,B,C,D be 4x, 7x, 3x and 1x respectively

So the number of ‘B’ blocks is 7*50 = 350.

Let the number of chocolates be 5x and the number of ice-cream cones be 8x.

Therefore, number of ice-cream cones in the box = 8*6 = 48.

## Introduction to Proportion

A lot of questions on ratio are solved by using proportion.

## Definition & Notation

a, d are called the extremes and b, c are called the means.

For a proportion a:b = c:d, product of means = product of extremes → b*c = a*d.

Let us take a look at some examples:

Number of litres of sugar solution in the mixture = (1/(1+2)) *45 = 15 litres.

So, 45-15 = 30 litres of salt solution is present in it.

Let the quantity of sugar solution to be added be x litres.

sugar solution / salt solution = (15+x)/30 = 2/1 → x = 45.

Therefore, 45 litres of sugar solution has to be added to bring it to the ratio 2:1.

Let the quantity of sugar required be x kgs.

3 kgs of sugar added to 6 kgs of flour constitutes a total of 9 kgs of sweet.

Therefore, 20 kgs of sugar is required for 60 kgs of sweet.

## Problems on Mixtures / Blends

Let x ml of chlorine be present in water.

Then, 12/100 = x/60 → x = 7.2 ml

Therefore, 7.2 ml is present in 60 ml of water.

Then, 8/100 = 7.2/y → y = 90 ml.

So in order to get a 8% chlorine solution, we need to add 90-60 = 30 ml of water.

Then, (4+x)/(20+x) = 50/100 → x = 12 L of bleach is added.

Now, there is 4+12 = 16 L of bleach in 16 L of water in a total of 32 L of solution.

16 L of bleach constitutes 20% of the solution →

## Practice Questions in Ratio and Proportion

A. 10 cm B. 12 cm C. 96 cm D. 8 cm

1cm/12 km = x cm/100 km → x = 8 cm

## 12 thoughts on “Ratio and Proportion Questions & Word Problems | GMAT GRE Maths”

Hey can you please emphasize on the working of the cashews and walnuts question?

Why do they have to be added to cancel out eaach other?

dining room = d family room = f

Lets make that ratio easier to handle: d : f = 4 : 6

Lets say 1 part = k, therefore d : f = 4k : 6k

Remember that the dining room is 4k so its size is:

Therefore ratio of boys to teacher is 4:1

Now for 9 (4 male+5 female) teachers, there are total 90 students which has 36(90*0.4) boys

This means for a group of 36 boys, there are 4 male teachers.

Hence the ratio of boys to male teacher is 36:4 or 9: 1

Worker(lamp)=3 Time=80 hours Object = 4 liters

Worker(lamp)=6 Time=40 hours Object= x

6R40=X (Rate is 1/60 from previous). 6(1/60)40=x (240/60)=x and x=4

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## Ratios and proportions and how to solve them

A ratio can be written in three different ways and all are read as "the ratio of x to y"

A proportion is read as "x is to y as z is to w"

$$\frac{x}{y}=\frac{z}{w} \: where\: y,w\neq 0$$

If one number in a proportion is unknown you can find that number by solving the proportion.

If we write the unknown number in the nominator then we can solve this as any other equation

$$\frac{x}{100}=\frac{2}{20}$$

$${\color{green} {100\, \cdot }}\, \frac{x}{100}={\color{green} {100\, \cdot }}\, \frac{2}{20}$$

If we again use the example with the cookie mix used above

$$\frac{{\color{green} {20}}}{{\color{blue} {1}}}=\frac{{\color{blue} {40}}}{{\color{green} {2}}}$$

$${\color{blue} {1}}\cdot {\color{blue} {40}}={\color{green} {2}}\cdot {\color{green} {20}}=40$$

It is said that in a proportion if

$$20\cdot 1:4=20\cdot \frac{1}{4}=5$$

## Video lesson

$$\frac{x}{x + 20} = \frac{24}{54}$$

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Here is an example of calculating ratios and proportions in word problems.

Note that you also may have used

The answer will be the same. Now simply plug into the equation for each instance.

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This math video tutorial provides a basic introduction into ratio and proportion word problems. Here is a list of examples and practice

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