Wednesday, 3 May 2017

Ratio and Proportion I - Ratio and Proportion Formulas for IBPS PO and SSC CGL Exams

Solve Ratio and Proportion Problems using Ratio and Proportion formulas for IBPS PO and SSC CGL Exams

Ratio and Proportion Formula

Ratios and Proportions is an important concept from the point of view of IBPS PO and SSC CGL Exams. Ratio and Proportion Formulas are used to solve Time and Work, Time and Distance, Averages etc. The concept of Ratio and Proportion speeds up problem-solving in competitive exams. 

In this post, we will discuss the concept of Ratio and Proportion and will solve questions using Ratio and Proportion Formulas.

What is a Ratio?

The ratio is a comparison of two like terms in its simplest form.

For example, we can compare the height of Ram and Shyam, We can compare the weight of Ram and Shyam, but we can't compare the height of Ram to the weight of Shyam.

A Ratio is denoted as a:b or a/b where a is the antecedent and b is the consequent.
Ratio and Proportion Formula
The two dots in the horizontal line are a colon which means " is to."
Suppose a is 40 kg and b is 60 kg then the ratio of a and b will be written as 40:60
As the ratio is the comparison of two terms in its simplest form.
We can denote 40:60 = 2:3
Ratio and Proportion Formula

Example of a Question Solved using Ratio and Proportion Formula

Question:  A company "A" sells a 53cm model T.V. at the price of Rs.7000 whereas another company "B" sells the same model at a price of Rs.16,800. What is the ratio of their respective prices?

Step 1:
As we need to compare the prices of the two companies we take the ratio of their selling prices
A : B where A = 7000 ; B = 16800

Step 2:
Writing A and B as a ratio- 
7000: 16800

Step 3:
A ratio is the comparison of two like terms in its simplest form we simplify,
7000: 16800
5: 12

Therefore, the ratio of the prices of the Company A and Company B is 5: 12.

Don't waste your time in writing the steps, directly substitute the values in the formulas and simplify the ratios.

What is a Proportion?

Proportion is an equality between two ratios.
i.e. a: b :: c : d

Where a, b, c, and d are said to be in proportion.
a, b, c and d are referred to as first, second, third and fourth proportional respectively.

a and d are called Extreme Proportion and b and c are called Mean Proportion.

As we know a: b can be written as a/b
we can write a/b = c/d

As the terms are equal we cross multiply,
ax d = b x c
The product of extremes should be equal to the product of means.
Ratio and Proportion Formula
Module 1: Solving Basic Questions using Ratio and Proportion Formulas

Question: In an entrance test, the ratio of appeared to successful students was 21: 11. Find the number of successful students 1176 students appeared in the test.

Step 1:
Appeared: Successful
21: 11

Step 2:
As we need to find the number of successful students, we need to cross multiply the number of appeared students with the ratio of successful students and the unknown number of successful students, with the ratio of appeared students to find the number of successful students.
Ratio and Proportion Formula
By cross multiplication we get,
(1176 x 11) / 21
= 616

Therefore, the number of successful students is 616.

Question: The ratio of boys and girls studying in a school is 17:18. If the boys are 150 less than the girls, what is the total number of girls?

Step 1:
The ratio of boys to girls is

Step 2:
We know that the boys are 1 unit less in ratio to girls and that 1 unit is given as 150.
So, 1 part = 150 students.

Step 3:
The number of girls studying in school- 
= 18 (as it is the ratio of girls) x 150
= 2700
Therefore, There are 1800 girl students in the school.

Module 2: An Example of Distribution of Amount Among the given People by using the Ratio and Proportion Formulas

Question: A profit of Rs.8000 is to be distributed among A, B and C in the ratio 5:2:3 respectively. What is the difference between the shares of A and B?

Regular Method:
Step 1:
Total amount = 8000
Ratio = 5 : 2 : 3

Step 2:
A = 5/10 (By converting ratios into fractions)
B = 2/10 (By converting ratios into fractions)
C = 3/10 (By converting ratios into fractions)

Step 3:
A = 5/10 x 8000 = 4000
B = 2/10 x 1600 = 1600

Step 4:
A - B = 4000 - 1600 = 2400

Therefore, the difference between  A and B is 2400

Smart Method:
Step 1:
As we know the total addition of ratio is equal to 8000
i.e. 10 parts = 8000
1 part = 800

Step 2:
The difference between A and B = 5 - 2 = 3 parts.

Step 3:
3 parts x 800
= 2400

Therefore, the difference between A and B is 2400.

Stay tuned for our next post and don't forget to write in the comment section on how this post helped you to solve ratio and proportion questions with ease.
Ratio and Proportion Formula
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