Question

❤Question❤

=> The sum of numerator and denominator of a fraction is three less
than twice the denominator. If each denominator and denominator is decreased
by 1, the fraction becomes 72. Find the fraction. (CBSE 2010-3M)

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Answer 1

Accurate question: The sum of numerator and denominator of a fraction is three less than twice the denominator. If each denominator and numerator is decreased by 1, the fraction becomes ½. Find the fraction. (CBSE 2010-3M.)

Let the fraction be = $\frac{a}{b}$

∴ Sum of numerator and denominator = $a + b$

According to question,

$a + b = 2b - 3$

$⇒ a = 2b - b - 3 = b - 3$

∴ We can also write the fraction as = $\frac{b - 3}{b}$

Also it is provided,

$\frac{(b - 3) - 1}{(b) - 1} = \frac{1}{2}$

By cross multiplication,

$\implies 2(b - 4) = b - 1$

$\implies 2b - 8 = b - 1$

$\implies 2b - b = - 1 + 8 = 7$

$\implies b = 7$

Now, putting the values,

Fraction = $\frac{a}{b} = \frac{b - 3}{b} = \frac{7 - 3}{7} = \frac{4}{7}$ (answer).