Question

The numerator of a fraction is 3 less than its denominator. If we add 1 to both numerator and denominator, it becomes equal to 4/5. Find the fraction.

Answer 1

Answer:

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Answer 2

Answer :

11/14

Solution :

Let denominator be ' x '

Then it's numerator will be ' x - 3 '

Now,

According to Question :

$\sf \dfrac{ x - 3 + 1}{ x + 1} = \dfrac{4}{5}$

$\sf\implies 5(x - 3 + 1) = 4(x+1)$

$\sf\implies 5x - 15 + 5 = 4x + 4$

$\sf\implies 5x - 4x = 4+15 - 5$

$\sf\implies x = 19 - 5$

$\sf\therefore x = 14$

Hence, denominator is 14 and numerator = 14 - 3 = 11

$\sf So, \:fraction\: is\: \dfrac{11}{14}$

_________

To check :

Numerator is 3 less than denominator.

= 14 - 11

= 3

Also,

if we add 1 to both numerator and denominator it becomes 4/5.

=> 11+1/14+1

=> 12/15

=> 4/5

Hence verified!

$\rule{200}2$