Question

A bicycle dealer was asked how many bikes he had in stock. He answered, “If one-half,

one-third, and one-quarter of the number of bikes were added together, they would make

13.” How many bikes did he have in stock?

Answer 1

Solution:

Let the total number of bikes in stock be $x$.

Now, according to question,

$\dfrac 12x+\dfrac 13x+\dfrac 14x=13$

$\Rightarrow x(\dfrac {6+4+3}{12})=13 \\\Rightarrow x(\dfrac {13}{12})=13 \\\Rightarrow x=13\times (\dfrac {12}{13}) \\\Rightarrow x=12$