If 2 and 3 are respectively added to the numerator and the denominator of a fraction- the fraction becomes 7-9 and if both the numerator as well as the denominator is decreased by 1 - the fraction becomes 4-5- What is the original fraction-

The correct option is A (5/6) Let the fraction be x/y. Then, x + 2/y + 3 = 7/9⇔ 9x 7y = 3 and x 1/y 1 = 4/5⇔ 5x 4y = 1 Solving we get x = 5, y = 6 ...

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Standard IX

Mathematics

Method of Cross Multiplication

If 2 and 3 ar...

Question

If 2 and 3 are respectively added to the numerator and the denominator of a fraction, the fraction becomes $\frac{7}{9}$ and if both the numerator as well as the denominator is decreased by 1, the fraction becomes $\frac{4}{5}$ . What is the original fraction?

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Solution

The correct option is A
(5/6)

Let the fraction be x/y.

Then, $\frac{x + 2}{y + 3} = \frac{7}{9} \Leftrightarrow 9 x - 7 y = 3$

and $\frac{x - 1}{y - 1} = \frac{4}{5} \Leftrightarrow 5 x - 4 y = 1$

Solving we get x = 5, y = 6

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If 2 and 3 are respectively added to the numerator and the denominator of a fraction, the fraction becomes 79 and if both the numerator as well as the denominator is decreased by 1, the fraction becomes 45. What is the original fraction?

The correct option is A (5/6) Let the fraction be x/y. Then, x+2y+3=79⇔9x−7y=3 and x−1y−1=45⇔5x−4y=1 Solving we get x = 5, y = 6

If 2 and 3 are respectively added to the numerator and the denominator of a fraction, the fraction becomes $\frac{7}{9}$ and if both the numerator as well as the denominator is decreased by 1, the fraction becomes $\frac{4}{5}$ . What is the original fraction?

The correct option is A
(5/6)

Let the fraction be x/y.

Then, $\frac{x + 2}{y + 3} = \frac{7}{9} \Leftrightarrow 9 x - 7 y = 3$

and $\frac{x - 1}{y - 1} = \frac{4}{5} \Leftrightarrow 5 x - 4 y = 1$

Solving we get x = 5, y = 6