Question

The sum of the numerator denominator of a fraction is 12 if the denominator is increased by 3 the fraction become1/2find the fraction

Answer 1

Answer:

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Answer 2

• Let numberator be N and denominator be D.

• Fraction = $\frac{N}{D}$

» The sum of the numerator denominator of a fraction is 12.

→ N + D = 12

→ N = 12 - D _________ (eq 1)

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» If the denominator is increased by 3 the fraction become 1/2.

Now..

Denominator = D + 3

A.T.Q.

→ $\dfrac{N}{D\:+\:3}$ = $\dfrac{1}{2}$

Cross-multiply them

→ 2N = D + 3

→ 2(12 - D) = D + 3 [From (eq 1)]

→ 24 - 2D = D + 3

→ - 2D - D = 3 - 24

→ 3D = 21

→ D = 7

Put value of D in (eq 1)

→ N = 12 - 7

→ N = 5

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$\dfrac{N}{D}\:=\:\dfrac{5}{7}$

_________ [ ANSWER ]

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✡ VERIFICATION :

$\dfrac{N}{D\:+\:3}$ = $\dfrac{1}{2}$

From above calculations we have N = 5 and D = 7. Put value of N and D in above equation

=> $\dfrac{5}{7\:+\:3}$ = $\dfrac{1}{2}$

=> $\dfrac{5}{10}$ = $\dfrac{1}{2}$

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

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