Question

a fraction becomes ,if 2 is added to both numerator and denominaotor.if 3 is added is added to both numerator and denominator it becomes.find the fraction

Answer 1

Correct Question:

A fraction becomes $\frac{9}{11}$ if 2 is added to both the numerator and the denominator if 3 is added to both numerator and denominator it's become $\frac{5}{6}$ find the fraction

Answer:

• The fraction is $\frac{7}{9}$

To Find:

• The Fraction.

Solution:

Let, the numerator be x and the denominator be y.

If 2 is added to both numerator and denominator, the fraction becomes 9/11.

【7+2/9+2 = 9/11】

→ $\frac{x+2}{y+2} = \frac{9}{11}$

→ $11(x+2) = 9(y+2)$

→ $11x+22 = 9y+18$

→ $9y-11x = 22-18$

→ $9y - 11x = 4$

→ $9y = 4+11x$

→ $y = \frac{(4+11x)}{9}$

If 3 is added to both numerator and denominator, the fraction becomes 5/6.

【7+3/9+3 = 10/12 = 5/6】

→ $\frac{x+3}{y+3} = \frac{5}{6}$

→ $6(x+3) = 5(y+3)$

→ $6x+18 = 5y+15$

→ $5y = 6x+18-15$

→ $5y = 6x+3$

→ $y = \frac{(6x+3)}{5}$

→ $\frac{(4+11x)}{9} = \frac{(6x+3)}{5}$

→ $5(4+11x) = 9(6x+3)$

→ $20+55x = 54x + 27$

→ $55x-54x = 27-20$

→ $x = 7$

→ $y = \frac{(4+11(7))}{9}$

→ $= \frac{(4+77)}{9}$

→ $= \frac{81}{9}$

→ $= 9$

Therefore,

● x = 7 and y = 9

The fraction = $\frac{7}{9}$