Question

if the numerator of a fraction is multipled by 2 and the denominator increased by 2 it becomes 6/7 if instead we multiple the denominator by 2 and increase the numerator by 2 it reduces to 1/2 . what is the fraction?​

Answer 1

In the above Question , the following information is given -

If the numerator of a fraction is multipled by 2 and the denominator increased by 2 it becomes 6/7 .

If instead we multiple the denominator by 2 and increase the numerator by 2 it reduces to 1/2 .

To find -

What is the required fraction ?

Solution -

Let the required fraction be [ x / y ]

First Condition -

If the numerator of a fraction is multipled by 2 and the denominator increased by 2 it becomes 6/7 .

=> [ 2x / y + 2 ] = [ 6 / 7 ]

=> 14x = 6y + 12

=> 7x = 3y + 6 ............... { 1 }

Second Condition -

If instead we multiple the denominator by 2 and increase the numerator by 2 it reduces to 1/2 .

So ,

[ x + 2 / 2y ] = [ 1 / 2 ]

=> 2x + 4 = 2y

=> x + 2 = y

=> x = y - 2 .......... { 2 }

Substituting this equation 2 in Equation 1

=> 7 ( y - 2 ) = 3y + 6

=> 7y - 14 = 3y + 6

=> 4y = 20

=> y = 5

=> x = 5 - 2 = 3

Required Fraction -

=> [ x / y ]

=> [ 3 / 5 ]

Hence , the required fraction is 3 / 5 .

__________

Answer 2

Answer:

Let the fraction be

y

x

Given,

y+1

2x

=1 ⟹2x=y+1 -----(1)

2y

x+4

=

2

1

⟹x+4=y -----(2)

Solving (1) and (2), we get,

x=5 and y=9

∴

9

5

is the fraction