Question

Answer with explanation! ​

Answer 1

Answer:

Required fraction is 7 / 9.

Step-by-step explanation:

Let,

Original fraction be a / b, where a is the numerator and b is the denominator.

According to the question : If numerator is increased by 2 and denominator is increased by 3, a / b becomes 3 / 4.

= > ( Original numerator + 2 ) / ( Original denominator + 3 ) = 3 / 4

= > ( a + 2 ) / ( b + 3 ) = 3 / 4

= > 4( a + 2 ) = 3( b + 3 )

= > 4a + 8 = 3b + 9

= > 4a = 3b + 1

= > a = ( 3b + 1 ) / 4 ...( 1 )

Also, if numerator is decreased by 3, denominator is decreased by 6, fraction becomes 4 / 3.

= > ( a - 3 ) / ( b - 6 ) = 4 / 3

= > 3( a - 3 ) = 4( b - 6 )

= > 3a - 9 = 4b - 24

= > 3a - 4b = 9 - 24

= > 3a - 4b = - 15

= > 3( 3b + 1 ) / 4 - 4b = - 15 { from ( 1 ) }

= > ( 9b + 3 - 16b ) / 4 = - 15

= > ( 3 - 7b ) = - 60

= > 7b = 63

= > b = 9

Thus,

= > 3a - 4b = - 15 { from above }

= > 3a - 4( 9 ) = - 15

= > 3a - 36 = - 15

= > 3a = 36 - 15

= > 3a = 21

= > a = 7

Hence the required fraction is a / b i.e. 7 / 9.

Answer 2

» In a fraction if numerator is increased by 2 and denominator is incresed by 3, it becomes 3/4.

• Let numerator be N and denominator be D.

• And Fraction = $\dfrac{N}{D}$

New numerator = N + 2

New denominator = D + 2

A.T.Q.

=> $\dfrac{N\:+\:2}{D\:+\:3}\:=\:\dfrac{3}{4}$

Cross-multiply them

=> 4(N + 2) = 3(D + 3)

=> 4N + 8 = 3D + 9

=> 4N - 3D = 1 _________ (eq 1)

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» If numerator is decreased by 3 and denominator is decresed by 6, fraction becomes 4/3.

New numerator = N - 3

New denominator = D - 6

A.T.Q.

=> $\dfrac{N\:-\:3}{D\:-\:6}\:=\:\dfrac{4}{3}$

Cross-multiply them

=> 3(N - 3) = 4(D - 6)

=> 3N - 9 = 4D - 24

=> 3N - 4D = - 15 ________ (eq 2)

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• Multiply (eq 1) by 3 and (eq 2) by 4

=> 4N - 3D = 1 (× 3)

=> 12N - 9D = 3 ________ (eq 3)

=> 3N - 4D = - 15 (× 4)

=> 12N - 16D = - 60 _______ (eq 4)

• Subtract (eq 3) from (eq 4)

=> 12N - 16D - (12N - 9D) = - 60 - 3

=> 12N - 16D - 12N + 9D = - 63

=> - 7D = - 63

=> D = 9

• Put value of D in (eq 1)

=> 4N - 3(9) = 1

=> 4N - 27 = 1

=> 4N = 28

=> N = 7

Fraction = $\dfrac{7}{9}$

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Sum of numerator and denominator is 16 (7 + 9)

Option a)

___________ [ANSWER]

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