Question 98

Sum of numerator and denominator of a fraction is 13. Adding 3 and 9 to the numerator and denominator respectively, the fraction becomes 2/3. What is the product of the numerator and denominator of the original fraction?

Solution

Let the numerator be x and denominator be y

$$x + y = 13$$, $$x=13-y$$ ------ i

According to the question,

$$\frac{(x+3)}{(y+9)}=\frac{2}{3}$$

$$3x + 9$$=$$2y+18$$

$$3x-2y$$=$$9$$ -------ii

From i and ii,

$$3(13-y)-2y$$=$$9$$

$$39-3y-2y$$=$$9$$

$$-5y$$=$$-30$$

$$y=6$$

So, $$x=7$$

Required product = 42

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