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Question

A fraction becomes 45 if one is added to both numerator and denominator. If 5 is subtracted from the numerator and denominator, the resultant fraction becomes 12. Find the fraction.

A
79
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B
710
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C
710
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D
None of the above
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Solution

The correct option is D None of the above
Let x be the numerator and y be the denominator.
Then, it is given that
(x+1)(y+1)=45;(x5)(y5)=12
(x+1)(y+1)=455x+5=4y+45x4y+1=0.(1)
(x5)(y5)=122x10=y52xy5=0.(2)
Multiplying (2) by 4, we get
8x4y20=0(3)
Subtracting (3) from (1), we get
3x+21=0
x=7
Putting x = 7 in (2), we get
2×7y5=0
y=9
Therefore, the fraction is 79.

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