Question

10. The numerator of a fraction is 4 less than the denominator. If I is added to both its
secton-3
numerator and denominator, it becomes . Find the fraction.​

Answer 1

Let the numerator and denominator of the fraction be x and y respectively. Then the fraction is x/y

The numerator of the fraction is 4 less the denominator. Thus, we have

x = y – 4

⇒ x – y = − 4

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

y + 1 = 8(x - 2)

⇒ y + 1 = 8x – 16

⇒ 8x – y = 1 + 16

⇒ 8x – y = 17

So, we have two equations

x – y = - 4

8x – y = 17

Here x and y are unknowns. We have to solve the above equations for x and y. Subtracting the second equation from the first equation, we get

(x – y) – (8x – y) = – 4 – 17

⇒ x − y − 8x + y = −21

⇒ −7x = −21

⇒ −7x = −21

⇒ x = 21/7

⇒ x = 3

Substituting the value of x in the first equation, we have

3 – y = – 4

⇒ y = 3 + 4

⇒ y = 7

Hence the fraction is 3/7