Question

A fraction becomes. 1/3
, if 2 is added to both of its numerator and
denominator. If 3 is added to both of its numerator and denominator,
then it becomes 2/5. Find the fraction.
​

Answer 1

Answer:

Step-by-step explanation:

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Let numerator= x

Let denominator= y

ATQ    x+2/y+2=1/3

          3x+6=y+2

           y=3x+4..........(i)

x+3/y+3=2/5

5x+15=2y+6

Putting  (i)

5x+15=2(3x+4)+6

15=6x+8+6

1=6x

x=1/6

Putting x in (i)

y=3(1/6)+4

y=1/2+4

y=1+8/2

y=9/2

Fraction= x/y=1/6 / 9/2

1/6*2/9=1/2

Answer 2

Given

Fraction becomes ⅓ if 2 is added to both numerator & denominator.

Fraction becomes 2/5 if 3 is added to both numerator & denominator.

To Find

Original fraction

Solution

Let the numerator be N & denominator be D.

➸ Original fraction = N/D

A/q to first case :

➝ (N + 2)/(D + 2) = ⅓

➝ D + 2 = 3(N + 2)

➝ D + 2 = 3N + 6

➝ D = 3N + 6 - 2

➝ D = 3N + 4 ..( l )

A/q to 2nd case :

➝ (N + 3)/(D + 3) = 2/5

➝ 2(D + 3) = 5(N + 3)

➝ 2D + 6 = 5N + 15

➝ 2D = 5N + 15 - 6

➝ 2(3N + 4) = 5N + 9

➝ 6N + 8 = 5N + 9

➝ 6N - 5N = 9 - 8

➝ N = 1

Putting value in ( l )

➝ D = 3(1) + 4

➝ D = 3 + 4

➝ D = 7

Now finding original fraction :

➝ Original fraction = N/D

➝ Original fraction = 1/7

Therefore,

Original fraction = 1/7