Question

The denominator of a fraction is greater than its numerator by 18 . If 8 is added to both its numerator and denominator it reduced to 1/13 . Find the fraction?​

Answer 1

Step-by-step explanation:

Thanks for the A2A.

Let x be the numerator, then according to the question the fraction is x/(x+6).

Now,if we add 8 to the denominator the fraction becomes 1/3

i.e. x/(x+6+8) = 1/3

To find the fraction we need to solve the above equation

x/(x+6+8) = 1/3

x/(x+14) = 1/3

By cross multiplication, we get

3x = x + 14

=> 2x = 14

=> x = 14/2

=> x = 7

So the fraction will be 7/(7+6) = 7/13.

Answer 2

Answer:

Let the required fraction be x/y . Then, we have: y = x + 11 ⇒ y – x = 11 ……(i) Again, x+8 /y+8 = 3/4 ⇒4(x + 8) = 3(y + 8) ⇒4x + 32 = 3y + 24 ⇒ 4x – 3y = -8 ……(ii) On multiplying (i) by 4, we get: 4y – 4x = 44 On adding (ii) and (iii), we get: y = (-8 + 44) = 36 On substituting y = 36 in (i), we get: 36 – x = 11 ⇒ x = (36 – 11) = 25 ∴ x = 25 and y = 36 Hence, the required fraction is 25/36