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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.
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.
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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=58⇒8x+16=5y+5⇒8x−5y=−11.................(i)and x+1y+1=12⇒2x+2=y+1⇒2x−y=−1......................(ii)On multiplying (i) by 2 and (ii) by 8, we get16x−10y=−2216x−8y=−8(−) (+) (+)−2y=−14Or y=7On substituting value of y in equation (ii) , we get2x−y=−1⇒2x=6⇒x=3Hence, the required fraction is 37.
3/7
Let the numerator be x and denominator be y.Then, the required fraction is xyx+2y+1=58⇒8x+16=5y+5⇒8x−5y=−11.................(i)and x+1y+1=12⇒2x+2=y+1⇒2x−y=−1......................(ii)On multiplying (i) by 2 and (ii) by 8, we get16x−10y=−2216x−8y=−8(−) (+) (+)−2y=−14Or y=7On substituting value of y in equation (ii) , we get2x−y=−1⇒2x=6⇒x=3Hence, the required fraction is 37.
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