Q51. - Algebra 1

Question

In the figure, $x:y=2:3$ and $y:z=3:5$ If $x=10$ find the value of z.

A 15

B 20

C 25

D 30

Step-by-Step Solution

Answer

The value of z is 25.

Step 1. Understanding the concept of ratio.

A ratio is a number, which expresses one quantity as a fraction of the other.

For example, a ratio of 3 to 4 is $3:4$ or $\frac{3}{4}$.

Step 2. Simplifying the given equation.

Ratios given are: 

 $\begin{array}{l} x:y=2:3\\ \Rightarrow \frac{x}{y}=\frac{2}{3}\\ y:z=3:5\\ \Rightarrow \frac{y}{z}=\frac{3}{5}\end{array}$

Step 3. Solve the equations.

It is also given that $x=10$, plugging this value in the first equation we get:

 $\begin{array}{l} x:y=2:3\\ \Rightarrow \frac{x}{y}=\frac{2}{3}\\ \Rightarrow \frac{10}{y}=\frac{2}{3}\\ \Rightarrow 10\times 3=2\times y\\ y=\frac{10\times 3}{2}\\ y=15\end{array}$

Plugging this value of y into the second equation we get,

 $\begin{array}{l} y:z=3:5\\ \Rightarrow \frac{15}{z}=\frac{3}{5}\\ \Rightarrow 15\times 5=3\times z\\ \Rightarrow z=\frac{15\times 5}{3}\\ z=25\end{array}$

Thus the answer is $z=25$.