Question

The numerator of a fraction is 2 less than the denominator.If 5 is added to both the numerator and the denominator, the fraction becomes 4/5.The fraction is _______.​

Answer 1

Answer:

Correct option is

B

22

17

Let the denominator be x

Fraction=

x

x−5

x+3

x−5+3

=

5

4

x+3

x−2

=

5

4

5(x−2)=4(x+3)

5x−4x=12+10

x=22

So, numerator=x−5=22−5=17

and denominator=22

So, the original fraction=

22

17

Answer 2

Given: Numerator of a fraction is 2 less than the denominator

To find: The fraction

Assumption: Let the denominator be x

Numerator = x – 2

Therefore, the fraction (x - 2)/x

If one is added to the numerator and denominator, fraction becomes (x - 2 +1)/(x + 1) = (x - 1)/(x + 1)

Sum of the fractions = (x - 2)/x + (x - 1)/(x + 1)

Sum of the fractions = 19/15

Therefore,

Cross-multiplying we get,

30x2 – 30x – 30 = 19x2 + 19x

30x2 – 19x2 – 30x – 19x – 30 = 0

11x2 – 49x – 30 = 0

Now we need to factorise such that, on multiplication we get 330 and on substraction we get 49.

So, equation becomes,

11x2 – (55x – 6x) – 30 = 0

11x2 – 55x + 6x – 30 = 0

11x(x – 5) + 6(x – 5) = 0

(11x + 6)(x – 5) = 0

So, 11x + 5 = 0 or x – 5 = 0