A fraction becomes 1/2 when 1 is subtracted from its numerator and 1 i

1.	A fraction becomes 1/2 when 1 is subtracted from its numerator and 1 is added to its denominator. Also, it becomes 1/3 when 6 is subtracted from its numerator and 1 from the denominator, Find original fraction
Answer» Given: A fraction becomes 1/2 when 1 is subtracted from its numerator and 1 is added to its denominator ALSO, it becomes 1/3 when 6 is subtracted from its numerator and 1 from the denominator To find: The original Solution: Let, "x" be the numerator "y" be the denominator So, the original fraction = $\frac{x}{y}$ (1) When 1 is subtracted from the numerator and 1 is added to its denominator, we get: $\frac{x - 1}{y + 1} = \frac{1}{2}$ $\implies 2(x - 1) = y + 1$ $\implies 2x - 2 = y + 1$ $\implies 2x - y -3 = 0$ ...... (i) (2) When 6 is subtracted from the numerator and 1 is subtracted from its denominator, we get: $\frac{x - 6}{y - 1} = \frac{1}{3}$ $\implies 3(x - 6) = y - 1$ $\implies 3x - 18 = y - 1$ $\implies 3x - y -17 = 0$ ...... (ii) Now, Subtracting EQ. (i) from (ii), we get 3x - y - 17 = 0 2x - y - 3 = 0 - + + --------------------- x -14 = 0 ---------------------- ∴ x = 14 Substituting x = 14 in eq. (i), we get 2(14) - y - 3 = 0 ⇒ 28 - y - 3 = 0 ⇒ 25 - y = 0 ⇒ y = 25 Thus, $\boxed{\bold{The \:original\:fraction\:is\:\:\underline{\frac{14}{25}} }}\:.$ ----------------------------------------------------------------------------------------- Also View: Fraction becomes 1/3 if 1 is subtracted from both its numerator and denominator.If 1 is added to both numerator and denominator,it becomes 1/2.Find the fraction? brainly.in/question/6565876 If 2 is added to the numerator of a fraction becomes 1/2 and if 1 is subtracted from the denominator it becomes 1/3 find the fraction? brainly.in/question/8664105 the numerator of a fraction is less than its denominator by 8 . when one is added to the numerator and 2 is subtracted from the denominator the fraction obtained is 2/7. find the original fraction? brainly.in/question/5077320

A fraction becomes 1/2 when 1 is subtracted from its numerator and 1 is added to its denominator. Also, it becomes 1/3 when 6 is subtracted from its numerator and 1 from the denominator, Find original fraction

Answer»

Given:

A fraction becomes 1/2 when 1 is subtracted from its numerator and 1 is added to its denominator

ALSO, it becomes 1/3 when 6 is subtracted from its numerator and 1 from the denominator

To find:

The original

Solution:

Let,

"x" be the numerator

"y" be the denominator

So, the original fraction = $\frac{x}{y}$

(1) When 1 is subtracted from the numerator and 1 is added to its denominator, we get:

$\frac{x - 1}{y + 1} = \frac{1}{2}$

$\implies 2(x - 1) = y + 1$

$\implies 2x - 2 = y + 1$

$\implies 2x - y -3 = 0$ ...... (i)

(2) When 6 is subtracted from the numerator and 1 is subtracted from its denominator, we get:

$\frac{x - 6}{y - 1} = \frac{1}{3}$

$\implies 3(x - 6) = y - 1$

$\implies 3x - 18 = y - 1$

$\implies 3x - y -17 = 0$ ...... (ii)

Now, Subtracting EQ. (i) from (ii), we get

3x - y - 17 = 0

2x - y - 3 = 0

- + +

---------------------

x -14 = 0

----------------------

∴ x = 14

Substituting x = 14 in eq. (i), we get

2(14) - y - 3 = 0

⇒ 28 - y - 3 = 0

⇒ 25 - y = 0

⇒ y = 25

Thus, $\boxed{\bold{The \:original\:fraction\:is\:\:\underline{\frac{14}{25}} }}\:.$

-----------------------------------------------------------------------------------------

Also View:

Fraction becomes 1/3 if 1 is subtracted from both its numerator and denominator.If 1 is added to both numerator and denominator,it becomes 1/2.Find the fraction?

brainly.in/question/6565876

If 2 is added to the numerator of a fraction becomes 1/2 and if 1 is subtracted from the denominator it becomes 1/3 find the fraction?

brainly.in/question/8664105

the numerator of a fraction is less than its denominator by 8 . when one is added to the numerator and 2 is subtracted from the denominator the fraction obtained is 2/7. find the original fraction?

brainly.in/question/5077320