Question

Find the proper fraction for which twice the numerator added to 2 equals the denominator. Also, double of the denominator is 1 less than five times the numerator.

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let the numerator be 'x' and the denominator be 'y' (i.e., let the proper fraction be \(\frac{x}{y}\) ).
By the given condition,
2x + 2 = y - - - (1)
5x - 1 = 2y - - - (2)
Putting y = 2x + 2 in equation (2), We get:
2(2x + 2) = 5x - 1
$\Rightarrow$ 4x + 4 = 5x - 1
$\Rightarrow$ x = 5
$\therefore$ From (1)
y = 2x + 2 = 2 $\times$ 5 + 2 = 12
Therefore, the required fraction is $\frac{5}{12}$