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in Mathematics by (33.0k points)

The denominator of a fraction is greater than its numerator by 11. If 8 is added to both its numerator and denominator, it becomes 3/4 . Find the fraction.

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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 .

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