Question

in the figure below, b lies between a and c. find the location of b so that the ratio of ab to bc is 2 to 3.

Explanation:

Step1: Calculate the distance between A and C

$AC=33 - 18=15$

Step2: Divide the distance according to the ratio

The ratio of $AB$ to $BC$ is $2:3$, so the total number of parts is $2 + 3=5$. The length of $AB$ is $\frac{2}{5}\times AC$.
$AB=\frac{2}{5}\times15 = 6$

Step3: Find the location of B

Since $A = 18$ and $AB = 6$, the location of $B$ is $18+6=24$

Answer:

$24$