Question

The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, the denominator becomes eight times the numerator. Find the fraction.

Options

• `3/8`

• `3/7`

• `4/8`

• `2/7`

Answer 1

`3/7`

Explanation:

Let's assume the numerator of the fraction to be x and the denominator of the fraction to be y.

So, the required fraction is `x/y`

From the question it's given as,

The number of the fraction is 4 less the denominator.

Thus, the equation so formed is,

x = y – 4

⇒ x – y = – 4 ......(i)

And also it's given in the question as,

If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is 8 times the numerator.

Putting the above condition in an equation, we get

y + 1 = 8(x – 2)

⇒ y + 1 = 8x – 16

⇒ 8x – y = 1 + 16

⇒ 8x – y = 17 ......(ii)

Solving (i) and (ii),

Substracting the equation (ii) from (ii), we get

(x – y) – (8x – y) = – 4 – 17

⇒ x – y – 8x + y = – 21

⇒ – 7x = – 21

⇒ x = `21/7`

⇒ x = 3

Substituting the value of x = 3 in the equation (i), we find y

3 – y = – 4

⇒ y =  3 + 4

⇒ y = 7

Therefore, the fraction is `3/7`.