Question

If the numerator of a certain fraction is increased by 2 and the denominator by 1 the fraction becomes equal to 5/8 and if the numerator and denominator are each diminished by 1 the fraction becomes equal to 1/2 find the fraction

Answer 1

Answer:

8/15

Step-by-step explanation:

Let the fraction be x/y

Then according to the given conditions, we have

(x + 2)/ (y + 1) = 5/8

8 (x + 2) = 5 (y + 1)

8x + 16 = 5y + 5

8x – 5y = 5 – 16

8x – 5y = -11 … (i)

And,

(x – 1)/ (y – 1) = ½

2 (x – 1) = (y – 1)

2x – 2 = y – 1

2x – y = 1 … (ii)

Now, performing (i) – 4 x (ii) we get

8x – 5y = -11

8x – 4y = 4

(-)—(+)—(-)

-y = -15

y = 15

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

2x – 15 = 1

2x = 1 + 15

x = 16/2 = 8

Therefore, the fraction is 8/15.