Question

If 2 is added to the numerator and denominator the fraction becomes $\frac{9}{10}$ and if 3 is subtracted from the numerator and denominator it become $\frac{4}{5}$. Find the fraction.

• A. $\frac{7}{9}$.
• B. $\frac{5}{8}$.
• C. $\frac{7}{8}$.
• D. $\frac{1}{7}$.

Answer 1

The correct option is C

$\frac{7}{8}$.

Let the numerator be x and denominator be y.

According to condition 1

$\frac{x+2}{y+2}=\frac{9}{10}$

$\Rightarrow$ 10(x + 2) = 9(y + 2)

$\Rightarrow$ 10x + 20 = 9y + 18

$\Rightarrow$ 10x – 9y = -2 ………. (i)

According to condition 2

$\frac{x-3}{y-3}=\frac{4}{5}$

$\Rightarrow$ 5(x – 3) = 4(y – 3)

$\Rightarrow$ 5x – 15 = 4y – 12

$\Rightarrow$ 5x – 4y = 3 ………. (ii)

Multiplying equation (ii) by 2, we get

10x – 8y = 6 ………. (iii)

Subtracting (i) and (iii)

10x – 9y = -2

10x – 8y = 6
- y = - 8

$\Rightarrow$ y = 8

Substituting the value of y in equation (ii)

5x – 4 × (8) = 3

5x – 32 = 3

$\Rightarrow$ x = 7

Therefore, fraction is $\frac{7}{8}$.