Question

A fraction becomes 4/5 when 5 is added to its numerator and 1 is subtracted from its
denominator. It becomes 1/2 when 3 and 5
are subtracted from its numerator and
denominator. The numerator of the
fraction will be
(a) 4
(6511
(c) 10
(d) 9​

Answer 1

Answer:

Numerator of the fraction is 11.

Option (b) is the correct answer.

Step-by-step explanation:

Let's assume that, the numerator is x and the denominator is y.

According to the problem,

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

$=>5x + 25 = 4y - 4$  [by cross multiplication]

$=>5x - 4y + 29 = 0$  .  .  .  .  .  .  .  .  .  (i)

Also, $\frac{x - 3}{y - 5} = \frac{1}{2}$

$=> 2x - 6 = y - 5$  [by cross multiplication]

$=> y = 2x - 1$   .  .  .  .  .  .  .  .  .  .  .  .  (ii)

Putting value of y from equation (ii) into equation (i)

$=>5x - 4(2x -1) + 29 = 0$

$=>5x - 8x + 4 + 29 = 0$

$=>3x = 33$

∴ $x = 11$

Numerator of the fraction is 11.

Option (b) is the correct answer.