Question

A fraction become 19/23 if 2 is added to both numerator and denominator if 3 is added to both the numerator and denominator it become 5/6 find the fraction

Answer 1

Answer:

Step-by-step explanation:

Information :- This solution is based on Cross Multiplication.

Given :-

Fraction becomes 9/11 if 2 is added to both numerator and denominator.

If 3 is added to both numerator and denominator it becomes 5/6.

Solution :-

Let the Numerator be x                  

Let the Denominator be y                  

Fraction = x/y                  

According to the Question,                  

⇒ (x + 2)/y + 2 = 9/11                  

On Cross multiplying,                  

⇒ 11x + 22 = 9y + 18                  

Subtracting 22 from both sides,                  

⇒ 11x = 9y – 4                  

Dividing by 11, we get                  

⇒ x = 9y – 4/11 … (i)                  

Then,              

⇒ (x+3)/y +3 = 5/6 … (ii)                  

On Cross multiplying,                  

⇒ 6x + 18 = 5y + 15                  

Subtracting the value of x, we get                  

⇒ 6(9y – 4 )/11 + 18 = 5y + 15                  

Subtracting 18 from both the sides                  

⇒ 6(9y – 4 )/11 = 5y – 3                  

⇒ 54 – 24 = 55y – 33                  

⇒ –y = – 9                  

⇒ y = 9                  

Putting this value of y in equation (i), we get                  

⇒ x = 9y – 4                  

⇒ x = (81 – 4)/77                  

⇒ x = 77/11                  

⇒ x = 7                  

Hence, the  fraction is 7/9.

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