Question

the sum of denominator and numerator of a fraction is 3 less than twice the denominator if each of the numerator and denominator is denominator is decreased by 1 the fraction becomes 1/2 find the fraction ​

Answer 1

• Let numberator be N and denominator be D.

» The sum of denominator and numerator of a fraction is 3 less than twice the denominator.

A.T.Q.

→ N + D = 2N - 3

→ - N + D = - 3

→N - D = 3

→ N = 3 + D _________ (eq 1)

» If each of the numerator and denominator is denominator is decreased by 1 the fraction becomes 1/2.

A.T.Q.

→ $\dfrac{N\:-\:1}{D\:-\:1}\:=\:\dfrac{1}{2}$

Cross-multiply them

→ 2(N - 1) = D - 1

→ 2N - 2 = D - 1

→ 2N - D = - 1 + 2

→ 2N - D = 1

→ 2(3 + D) - D = 1 [From (eq 1)]

→ 6 + 2D - D = 1

→ D = - 5

Put value of D in (eq 1)

→ N = 3 - 5

→ N = - 2

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Fraction = 2/5

________ [ ANSWER ]

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✡ VERIFICATION :

From above calculations we have N = - 2 and D = - 5

Put value of N and D in this equation : $\dfrac{N\:-\:1}{D\:-\:1}\:=\:\dfrac{1}{2}$

=> $\dfrac{-2\:-\:1}{-5\:-\:1}\:=\:\dfrac{1}{2}$

=> $\dfrac{-3}{-6}\:=\:\dfrac{1}{2}$

=> $\dfrac{1}{2}\:=\:\dfrac{1}{2}$

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