# Number System V – List of Algebra Formulas to solve Algebra Questions

In this post, we will discuss Algebra Formulas with Algebra Questions from Number System using smart methods to save time in IBPS PO and SSC CGL Exams

Number system, being the foundation topic of mathematics has an important place in IBPS PO and SSC CGL Exams. Algebra questions are one of the important questions from number system that make their way in competitive exams. Algebra questions can be easily solved with the use of algebra formulas. In this post, we have discussed algebra formulas with few algebra questions that will help you save time in IBPS PO and SSC CGL Exam.

It would be a good idea to revise basics of number system before we move ahead with new concepts in this blog.
List of Algebra Formulas to solve Algebra Questions
Example to solve algebra questions using Algebra Formulas

Question: The difference between two numbers is 4 and the difference between their squares is 128. Which is the larger number?
1) 14              2)16          3) 12               4) 18               5) None of these

Regular Method
Solution:
Step 1:
Let us assume the larger number to be as – ‘L’
Let us assume the smaller number to be as – ‘S’
As mentioned in the question,
L – S = 4                              (i)
As mentioned in the question,
L2  S2 = 128

Step 2:
a2  b2 = ( a + b ) ( a – b)
L2  S2 = ( L + S ) ( L – S) = 128           (ii)

By substituting equation 1 in 2 we get,
(L + S ) 4 = 128
L + S = 128/4
L + S = 32                          (iii)

Step 3:
By adding equation 1 and 3 we get,
2L = 36
L = 18

Therefore, the correct answer is option 4: 18.

Smart Method
We can use the elimination method to solve this question which will help you solve questions within seconds without framing the equation.

Step 1:
Option 1- If the larger number is 14 then 10 should be the smaller number. By taking the difference of their squares we get 96. As it is not equal to 128 we can easily eliminate this option.
Option 2: If the larger number is 16 then 12 should be the smaller number. By taking the difference of their squares we get 112. As it is not equal to 128 we can easily eliminate this option.
Option 3: If the larger number is 12 then 8 should be the smaller number. By taking the difference of their squares we get 80. As it is not equal to 128 we can easily eliminate this option.
Option 4: If the larger number is 18 then 12 should be the smaller number. By taking the difference of their squares we get 128. As it is equal to 128 and satisfies our condition. Thus, this is the correct answer.
Example to solve algebra questions using Algebra Formulas

Question:
Solution:
Step 1:

This can be simplified as
Step 2: