5)A fraction becomes ī, if 2 is added to
both the numerator and the denominator.
If, 3 is added to both the numerator
and the denominator it becomes
Find the fraction.
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≡QUESTION≡
A fraction becomes 9/ 11 if 2 is added to both the numerator and the denominator if 3 is added to both numerator and denominator it's become 5/6 find the fraction.
║⊕ANSWER⊕║
Let the numerator of fraction be x and denominator be y .
Friction = x / y
First case : [ When 2 added in both ]
x + 2 / y + 2 = 9 / 11
11 x + 22 = 9 y + 18
11 x - 9 y = - 4 ... ( i )
Second case : [ When 3 added in both ]
x + 3 / y + 3 = 5 / 6
6 x + 18 = 5 y + 15
6 x - 5 y = - 3 ... ( ii )
Now Multiply by 6 in ( i ) and by 11 in ( ii )
66 x - 54 y = - 24
66 x - 55 y = - 33
[ Subtracting ( ii ) from ( i ) ]
y = 9
Now x = - 4 + 9 y / 11 ... ( i ) [ y = 9 ]
x = 77 / 11
= > 7
Now we have x = 7 and y = 9
Thus , fraction is 7 / 9 .
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