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Fraction whose numerator and denominator are changed: form equations and find it

This type of question, asked 2 times: CDS 1 2017, CDS 2 2021. All 2 questions below, oldest first.

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  1. Question 1

    CDS 1 2017

    25
    What number must be subtracted from both the numerator and the denominator of the fraction 2735\dfrac{27}{35} so that it becomes 23\dfrac{2}{3} ?

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  2. Question 2

    CDS 2 2021

    35
    The sum of numerator and denominator of a fraction is 10. If the numerator is increased by 3 and denominator is decreased by 1, the fraction becomes 1. What is the difference between numerator and denominator of the fraction ?

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