Multiple Choice Questions on A fraction becomes 1 3 when 1 is subtracted from both the numerator and the denominator Th........... for Mathematics - All Exams Preparation

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Multiple Choice Questions

A fraction becomes 1 3 when 1 is subtracted from both the numerator and the denominator Th...........

Quantitative Aptitude ( CCS) Number System
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    A fraction becomes 1/3, when 1 is subtracted from both the numerator and the denominator. The same fraction becomes  1/2, when 1 is added to both the numerator and the denominator. The sum of numerator and denominator of the fraction is 

    10

    Correct Answer

    18

    Incorrect Answer

    7

    Incorrect Answer

    16

    Incorrect Answer
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    Explanation:

    Let the original fraction be x/y

    According to the question, 
    (x-1)/(y-1)=1/3
    ⇒ 3x – 3 = y – 1 
    ⇒ 3x – y = 2 …(i) 
    And (x+1)/(y+1)=1/2
    ⇒ 2x + 2 = y + 1 
    ⇒ 2x – y = -1 …(ii)
    On subtracting equation (ii) from equation (i), we get 
    (3x – y) – (2x – y) = 2 – (-1) 
    ⇒ 3x – 2x = 3 
    ⇒ x = 3
    On putting the value of x in equation (i), we get
    3x – y = z 
    ⇒ 9 – y = 2 
    ⇒ y = 9 – 2 = 7 
    ∴ Sum of numerator and denominator 
    = x + y 
    = 7 + 3 = 10

    By: Amit Kumar
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