Question

If the numerator and denominator of 1/6 is increased by x, the result fraction is equal to 1/2
Find the value of x?

Answer 1

Answer:

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Let the fraction be

y

x

Then according to the given conditions, we have

(y+1)

(x+2

=

8

5

⇒8(x+2)=5(y+1)

⇒8x+16=5y+5

⇒8x−5y=5−16

⇒8x−5y=−11 … (i)

And,

(y−1)

(x−1)

=

2

1

⇒2(x−1)=(y−1)

⇒2x−2=y−1

⇒2x−y=1 … (ii)

Now, performing eq. (i) - 4 x eq. (ii) we get

(8x−5y)−(8x−4y)=−11−4

⇒−y=−15

⇒y=15

On substituting the value of y in eq. (ii), we get

2x−15=1

⇒2x=1+15

⇒x=

2

16

=8

Therefore, the fraction is

15

8

.