Question

• The numerator of a fraction is 4 less than its denominator . If the numerator is deceased by 2 and the denominator is increased by 1 , then the fraction becomes 1/8 . Find the fraction .

• What is the sum of two consecutive even numbers , the difference of whose square is 84 .
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Answer 1

Answer:

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Answer 2

᠂ SOLUTION (1) ᠂

• Let the denomintaor of the required fraction be x then numerator of the required fraction will be x - 4.
• Required Fraction = (x - 4)/x

◖ According to the Question Now ◗

⇢ (x - 4 - 2)/(x + 1) = 1/8

⇢ (x - 6)/(x + 1) = 1/8

⇢ 8(x - 6) = 1(x + 1)

⇢ 8x - 48 = x + 1

⇢ 8x - x = 1 + 48

⇢ 7x = 49

⇢ x = 49 ÷ 7

⇢ x = 7

◖ Required Fraction ◗

⇢ Required Fraction = (x - 4)/x

⇢ Required Fraction = (7 - 4)/7

⇢ Required Fraction = 3/7

∴ The required fraction will be 3/7.

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᠂ SOLUTION (2) ᠂

• Let the two consecutive even numbers be m, (m + 2)

◖ According to the Question Now ◗

↠(m + 2)² - m² = 84

↠m² + 2(m)(2) + (2)² - m² = 84

↠m² + 4m + 4 - m² = 84

↠4m + 4 = 84

↠4m = 84 - 4

↠4m = 80

↠m = 80 ÷ 4

↠m = 20

◖ Required Sum of two consecutive even numbers◗

↠m + 2 + m

↠20 + 2 + 20

↠ 40 + 2

↠ 42

∴ The required sum of two consecutive even numbers is 42.