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Question 3 (v)
Form the pair of linear equations for the following problems and find their solution by substitution method:
A fraction becomes 911, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 56. Find the fraction.

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Solution

Let Numerator = x
Denominator = y
Fraction will be xy

A fraction becomes 911, if 2 is added to both the numerator and the denominator.

(x+2)(y+2)=911

By cross multiplication, we get;
11x + 22 = 9y + 18
Subtracting 22 from both sides, we get
11x = 9y - 4
Dividing by 11, we get,
x=9y411 … (i)

Given that 3 is added to both the numerator and the denominator it becomes 56.

(x+3)(y+3)=56 … (ii)

By Cross multiplication, we get
6x + 18 = 5y + 15
Substituting the value of x, we get;
6(9y4)11+18=5y+15
Subtract 18 from both sides, we get;
6(9y4)11=5y3
54y24=55y33
-y = -9
y = 9

Putting this value of y in equation (i), we get,
x = 9y411 … (i)
x=(814)11
x=7711
x = 7

Hence, our fraction is xy = 79.

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