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Question

# If 2 is added to the numerator and denominator of a fraction, it becomes 9/10. If 3 is subtracted from the numerator and denominator of the same fraction, it becomes 4/5. What is the fraction?

A
56
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B
67
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C
78
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D
89
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Solution

## The correct option is C 78 Let the fraction is xy According to the condition 1: When 2 is added to the numerator and denominator of a fraction, then it equals 910 x+2y+2=910 ⇒10(x+2)=9(y+2)⇒10x+20=9y+18⇒10x−9y=−2 …(i) According to the condition 2: When 3 is subtracted from the numerator and denominator of the same fraction, then it equals 45 x−3y−3=45 5(x−3)=4(y−3)5x−15=4y−125x−4y=3 Multilying both the sides by 2 2(5x−4y)=2(3) 10x−8y=6 …(ii) Now, subtracting (ii)from(i) 10x−9y=−2 10x−8y=6 (-)_____________ −y=−8 −y=−8 y=8 Substituting the value of y=8 in (i), we get 10x−9(8)=−2⇒10x=−2+72⇒10x=70⇒x=7 x=7,y=8 Hence, the required fraction is 78.

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