Question

A fraction becomes 5/8 when 3 is added to both numerator and denominator. If 1 is subtracted from the numerator and 1 is added to the denominator, then it becomes 1/6 Find the fraction.​

Answer 1

x/y be fraction and after solving x/y=2/5

fraction is2/5

Answer 2

Answer- The above question is from the chapter 'Pair of Linear Equations in Two Variables'.

There are two ways to solve a pair of linear equations in two variables:

1) Graphical Method

2) Algebraic Method:

a. Substitution Method

b. Elimination Method

c. Cross-Multiplication Method

Given question: A fraction becomes $\frac{5}{8}$ when 3 is added to both numerator and denominator. If 1 is subtracted from the numerator and 1 is added to the denominator, then it becomes $\frac{1}{6}$ . Find the fraction.​

Solution: Let the numerator be x and denominator = y.

$\implies Fraction = \frac{x}{y}$

Ist Condition:

$\dfrac{x \: + \: 3}{y \: + \: 3} = \dfrac{5}{8}$

8x + 24 = 5y + 15

8x - 5y = - 9 --- (1)

2nd Condition:

$\dfrac{x \: - \: 1}{y \: + \: 1} = \dfrac{1}{6}$

6x - 6 = y + 1

6x - y = 7 --- (2)

Multiplying equation 2 by 5 on both sides, we get,

30x - 5y = 35 --- (3)

Equation 3 - Equation 1, we get,

22x = 44

x = 2

Put value of x = 2 in equation 2, we get,

y = 5

⇒ Fraction = $\frac{2}{5}$