Question

the numerator and the denominator of a fraction are in the ratio 6 ratio 7 is 4 is subtracted from the numerator and 1 is added to the denominator and new fraction is formed whose value is 7 upon 11 find the original fraction​

Answer 1

Answer:

Original Fraction = 6/7

Step-by-step explanation:

Let numerator be "6M" and denominator be "7M".

Four is subtracted from the numerator and one is added to the denominator then fraction becomes 7/11.

According to question,

⇒ $\dfrac{6M\:-\:4}{7M\:+\:1}\:=\:\dfrac{7}{11}$ ___ (eq 1)

Cross-multiply them

⇒ $11(6M\:-\:4)\:=\:7(7M\:+\:1)$

⇒ $66M\:-\:44\:=\:49M\:+\:7$

⇒ $66M\:-\:49M\:=\:7\:+\:44$

⇒ $17M\:=\:51$

⇒ $M\:=\:3$

So,

Numerator = 6M

⇒ 6(3)

⇒ 18

Denominator = 7M

⇒ 7(3)

⇒ 21

Fraction = $\dfrac{Numerator}{Denominator}$ = $\dfrac{18}{21}$

⇒ $\bold{\dfrac{6}{7}}$

∴ Original fraction is 6/7.

______________________________

Verification

From above calculations we have M = 3

Put value of M in (eq 1)

⇒ $\dfrac{6(3)\:-\:4}{7(3)\:+\:1}\:=\:\dfrac{7}{11}$

⇒ $\dfrac{18\:-\:4}{21\:+\:1}\:=\:\dfrac{7}{11}$

⇒ $\dfrac{14}{22}\:=\:\dfrac{7}{11}$

⇒ $\dfrac{7}{11}\:=\:\dfrac{7}{11}$

Answer 2

Answer:

18/21 [ original fraction ]

Step-by-step explanation:

Let the numerator be '6a' and

denominator be '7a'

then the fraction becomes 6a/7a

Given

fraction are in the ratio 6a : 7a

According to question

If 4 substracted from the numerator

and 1 added to the denomirator then

the new fraction formed by 7/11

i,e ( 6a - 4 )/( 7a + 1 ) = 7/11

11( 6a - 4 ) = 7( 7a + 1 )

66a - 44 = 49a + 7

66a - 49a = 7 + 44

17a = 51

a = 3

therefore the original fraction is

6a/7a = ( 6 × 3 )/( 7 × 3 ) = 18/21