• 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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᠂ 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.
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