**>>CLICK HERE TO DOWNLOAD PDF FILE of NUMBERS.**

Rules-based on Numbers is simple, no need to learn anything new. These are all, we have already done in our school times. Recall the Mathematical Formula in Algebra

The concept needs a better understanding and thorough reading of statements given to solve.

Let see how to figure out the number of based problems.....

**(a + b)**^{2}= a^{2}+ b^{2}+ 2ab**(a - b)**^{2}= a^{2}+ b^{2}-2ab**(a**^{2}- b^{2})= (a + b) (a - b)**(a + b)**^{3}= a^{3}+ b^{3}+ 3ab (a+b)**(a - b)**^{3}= a^{3}– b^{3}-3ab (a-b)**a**^{3}+ b^{3}= (a+b) (a^{2}- ab +b^{2})**a**^{3}- b^{3}= (a-b) (a^{2}+ ab +b^{2})**(a+b+c)**^{3}= a^{2}+ b^{2}+ c^{2}+ 2ab +2bc + 2caThe concept needs a better understanding and thorough reading of statements given to solve.

Let see how to figure out the number of based problems.....

**Problem1: The sum of two numbers is 29 and the difference of their squares is 145. The difference between the numbers is?**Solution:

**Step1:**Take two numbers X and Y

**Step2:**The sum of two numbers is 29

**X + Y = 29**

**Step3:**The difference of their squares is 145

**X**

^{2}– Y^{2}= 145**Step4:**To evaluate both the statements apply algebraic formula and put the given values here

**(a**

145 = 29 (a-b)

145/29 = (a-b)

^{2}- b^{2})= (a + b) (a - b)145 = 29 (a-b)

145/29 = (a-b)

**Step5:**The difference of the numbers (X - Y)= 5

**Problem2: The ratio between two numbers is 3:4 and their sum is 420. The greater of the two numbers is?**Solution:

Step1: Take a numbers x

**Step2:**The ratio between two numbers is 3:4

**Step3:**Ratio means both the numbers are divisible with single common multiple. Let’s take it ‘x’ which will multiply with both the numbers as

**First number = 3x**

Second Number = 4x

Second Number = 4x

**Step4:**Their sum is 420

**3x + 4x = 420**

7x= 420

x=60

7x= 420

x=60

**Step5:**Numbers are

**3x= 3 * 60= 180**

4x= 4 * 60 = 240

4x= 4 * 60 = 240

**Step6:**The second number is greater than first one

**Problem3: Three fourth of one-fifth of a number is 60. The number is?**

Solution:Solution:

Step1: Three fourth ¾ and one fifth 1/5

**Step2:**‘Of ’ designated multiplication here

**Step3:**A number takes it as ‘x’

**3/4 * 1/5 * x = 60**

3/20 * x = 60

x = 400

3/20 * x = 60

x = 400

**Step4:**The number is 400

**Problem4: The difference between the squares of two consecutive numbers is 35. The number are?**Solution:

Step1: Consecutive numbers are numbers follow each other like 1, 2,3 ,4

**Step2:**Imagine two consecutive number x and (x + 1)

**Step3:**The difference between the squares of two numbers is 35. Square it first x

^{2}, (x+1)

^{2}

**Step4:**The difference between two means subtract the smaller number from greater one i.e.

**(x+1)**

^{2}- x^{2}= 35**Step5:**Evaluate and it comes out x=18

**Step6:**First number x=18

Second number is x + 1 =19

**Problem5: The sum of the two numbers is twice their difference. If the one of the number is 10, the other number is?**Solution:

Step1: Take two number X and Y

**Step2:**Take X= 10 ( Given one number)

**Step3:**The sum of the two numbers is twice their difference.

**(10 + Y) =2 (10 –Y)**

10 +Y = 20 -2Y

Y= 10/3

10 +Y = 20 -2Y

Y= 10/3

**Step4:**Other number is 10/3 or take in mixed fraction as 3 1/3

**Take a number X**

Solution:

Step1:

*Problem6: The number whose fifth part is increased by 5 is equal to its fourth part diminished by 5. The number is?*Solution:

Step1:

**Step2:**Fifth part of number is 1/5 of x and fourth part of number is 1/4 of x

**Step3:**The number whose fifth part is increased by 5 is equal to its fourth part diminished by 5

**1/5 * x + 5 =1/4 * x -5**

**Step4:**Evaluate it

**x/5+ 5 = x/4 -5**

10 = x/4 – x/5

10 = x/4 – x/5

**Step5:**The number is x = 200

*Post on the Higher level difficulty in Numbers is coming soon.......***>>CLICK HERE TO DOWNLOAD PDF FILE of NUMBERS.**

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