Question

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Find the fraction which becomes 1/2 when it's numerator is increased by 6 and is equal to 1/3 when it's denominator is increased by 7​

Answer 1

$let \: the \: \: number \: be \: x \: and \: the \: denomitor \: be \\ \: y \: so \: the \: fraction \: will \: be \: \frac{x}{y}$

$according \: to \: the \: question \: \\ \frac{x + 6}{y} = \frac{1}{2}$

$\longrightarrow \: 2x \: - y \: = \: - 12 \: \: \: (1)$

and

$\frac{x}{y + 7} = \frac{1}{2}$

3x - y = 7

subtracting equation (2) from equation (1)

-x = -19

$\therefore \: x \: = \: 19$

substituting the value of x in equation (1)

we get, 2× (19) - y = -12

→ 38 + 12 = y

→ y = 50

$hence \: fraction \: is \frac{19}{50}$

most welcome my friend!

Answer 2

Step-by-step explanation:

Let the fraction be

y

x

.

The fraction becomes

2

1

when denominator is increased by 4.

Therefore,

y+4

x

=

2

1

⇒2x=y+4

2x−y=4 ....(1)

Now, the fraction is equal to

8

1

when numerator is diminished by 5.

Therefore,

y

x−5

=

8

1

⇒8x−40=y

⇒8x−y=40 ....(2)

Subtracting equations (1) and (2), we get

6x=36

⇒x=6

Putting this value in equation (1), we get

2(6)−y=4

⇒12−y=4

⇒y=8

Therefore, the fraction is

8

6