# Ratio and Proportions Math trick Problem and solution

## Ratio and Proportions Math trick Problem and solution

Ratio and Proportions Math trick Problem and solution

## Ratio:

A ratio is a fraction that compares two quantities that are measured in the same units.

Ratio of two quantities a and b of the same kind  is a/b is denoted by the a:b, and read as a is to b.

## Properties of the ratios:

1. The value of ratio never changed or we can say it is remains unchanged, if each of its terms are multiplied or divided by a same non-zero number.
2. For a>b, if the same positive number is added to each term, the ratio decreases.
3. For a<b, if the same positive number is added to each term, the ratio increases.

Check Also: Exam Jagat

## Part-to-Part Ratios:

The ratio that compares one part to another part is called part-to-part ratio, denoted by part:part.

Example: If a bag contains marbles of colors red and blue with quantities 3 & 5 respectively, then ratio of the red marbles is known as part:part ratio

This would be denoted as;

Red marbles: Blue marbles

=3:5

## Part-to-Whole Ratios:

If a set of objects is divided into two groups, in the ratio a:b, then the first group contains a/(a+b) objects and the second group contains b/(a+b) objects. This ratio is called part-to-whole ratio denoted as part:whole. Hence, the objects a and b would be a:(a+b) and b:(a+b) ratios with respect to the total objects.

Example: From recent example, the part-to-whole ratios can be shown as;

For red marbles= 3:8

For blue marbles= 5:8

## Note:

• Ratio is the relation existing between any two quantities of the same kind.
• Order of the terms in the ratio is important. in the general for a is not equal b, the ratio a:b and b:a are different.
•  Ratio of two quantities is an absolute number if it has no unit.

In a partnership if the investment are in the ratio a:b and the periods are in the ratio m:n, then they share the profits in the ratio am:bn.

## How to Determine a Ratio:

Ratio represent how one number is related to another number.

A ratio may be written as A:B or A/B or by the phrase “A to B” .

A ratio of 1:5 says that the second number is five times as large as the first.

The following steps will allow a ratio to be determination if two numbers are known.

Example :

Determine the ratio of 24 to 40.

Divided both terms of the ratio by the greatest common factor ( 24/8=3,  40/8=5)

The ratio of 24 to 40 is 3:5

• Ratio is another name of the fraction. An equation in which two ratio are equal is called a proportions.
• Ratio is a quotient of one number a to another number b. It can be expressed in three ways.
1. a:b
2. a/b
3. a÷b

The ratio a:b is read as a to b.

Example: Find the ratio of x to y from the equation 3x²+y²=4xy

Solution x²-4xy+y²=0

(x-y)(3x-y)=0
hence either x-y=0
x=y
x:y=1:1 or x∕y= 1
3x-y=0
3x=y
x:y= 1:3
or x/y=1/3
The ratio of x to y is 1 to 1, or 1 to 3.
Example: If 4 boys can paint a fence in 5 hours. how many hours would it take 3 boys to paint the same fence?
Solution. This problem involves the concepts of inverse relationship.
Here, if more number of boys are there, the time taken to paint the fence will be less and if less number of boys are there , the time taken will be more.
Now,It is given that 4 boys paint a fence in 5 hours.
Let x be the number of hours that is taken by 3 boys to paint the fence.
Here,
4/3 = x/5
x=(4×5)/3
x= 20/3