Question

When 1 is added to the numerator of a fraction it becomes 1/4 and 1 is subtracted from th
denominator of that fraction it becomes 1/5. Find the fraction.
A) 4/19 B) 3/16 C 5/17 D) 2/15 E)​

Answer 1

Answer:

B) 3 / 16

The fraction is 3 / 16

Explanation:

Let,

Numerator of a fraction =  x

Denominator of fraction  = y

Fraction = x / y

1 is added to the numerator of a fraction it becomes 1/4

So,

⇒  $\frac{x + 1}{y} \: = \: \frac{1}{4}$

⇒  4 (x + 1)  =  1y

⇒  4x + 4 = y

⇒  4x - y = - 4   ------------------(1)

•  1 is subtracted from the denominator of  fraction it becomes 1/5

⇒  $\frac{x}{y - 1} \: = \: \frac{1}{5}$

⇒  5x = y - 1

⇒  5x - y = -1  --------------------(2)

Solving equations (1) and (2)

★  Substraction :

$\begin{array}{c c c c c}4x &-&y&=&-4 \\5x &-&y&=&-1\\(-)&(+)&&&(+)\\\end{array}\\\rule{110}{1}\\\begin{array}{c c c c c} &&x&=&3\end{array}\\\rule{110}{1}$

So,

⇒  x = 3

★  put x = 3   equ. (1)

⇒  4 (3) - y = - 4

⇒  12 - y = - 4

⇒  - y = - 4 - 12

⇒  - y =  - 16

⇒  y  =  16

Therefore,

⇒  x = 3

⇒  y = 16

.°.  The fraction is 3 / 16

Answer 2

SOLUTION :-

•Let,

=>Numerator of a fraction is "r" .

=>Denominator of a fraction is "s" .

And fraction is r / s.

Case (I)

•When 1 is added to the numerator of a fraction it becomes 1/4 .

$\: => \: \frac{r + 1}{s} = \frac{1}{4}$

=> 4( r +1 ) = s

=> 4r + 4 = s

=> s = 4r + 4 ------(1)

Case (II)

•1 is subtracted from the denominator of that fraction it becomes 1/5.

$=> \: \frac{r}{s - 1} = \frac{1}{5}$

=> 5r = 1( s - 1)

=> 5r = s -1

=> 5r -s = -1 ---------(2)

Put eqn.(1) value in eqn.(2)

=> 5r - (4r + 4) = -1

=> 5r - 4r - 4 = -1

=> r = -1 + 4

=> r = 3 .

Put r = 3 in eqn. (1)

=> s = 4(3) + 4

=> s = 12 + 4

=> s = 16 .

Therefore, the fraction is (b) 3/16 .