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

**(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:**

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

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

Solution:

**Step1:** Take a number X**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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