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    If the numerator of a fraction is increased by 30% and its denominator is decreased by 35%, the value of the fraction becomes315\frac{3}{15}153​​. Fin
    Question

    If the numerator of a fraction is increased by 30% and its denominator is decreased by 35%, the value of the fraction becomes315\frac{3}{15}​. Find the original fraction.

    A.

    310\frac{3}{10}​​

    B.

    15\frac{1}{5}​​

    C.

    110\frac{1}{10}​​

    D.

    35\frac{3}{5}​​

    Correct option is C

    Given:

    Numerator increased by 30%.

    Denominator decreased by 35%.

    New fraction = 315=15\frac{3}{15} = \frac{1}{5}

    Solution:

    Let the original fraction be xy\frac{x}{y}​ .

    After changes:

    x+0.3xy0.35y=15\frac{x + 0.3x}{y - 0.35y} = \frac{1}{5}​​

    1.3x0.65y=15\frac{1.3x}{0.65y} = \frac{1}{5}​​

    5×1.3x=0.65y 6.5x=0.65y  y=10x5 \times 1.3x = 0.65y\\ \ \\ 6.5x = 0.65y \\ \ \\\implies y = 10x​​

    Original fraction:

    xy=x10x=110\frac{x}{y} = \frac{x}{10x} = \frac{1}{10}​​

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