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Question

If the numerator of a fraction is increased by 2 and the denominator by 1, it becomes 5/8 and if the numerator and denominator of the same fraction are each increased by 1, the fraction becomes 1/2. Find the fraction.


A

2/7

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B

3/7

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C

2/5

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D

4/5

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Solution

The correct option is B

3/7


Let the numerator be x and denominator be y.Then, the required fraction is xyx+2y+1=588x+16=5y+58x5y=11.................(i)and x+1y+1=122x+2=y+12xy=1......................(ii)On multiplying (i) by 2 and (ii) by 8, we get16x10y=2216x8y=8() (+) (+)2y=14Or y=7On substituting value of y in equation (ii) , we get2xy=12x=6x=3Hence, the required fraction is 37.


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