Chapter 2: Q51. (page 117)

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

Short Answer

Expert verified

The value of z is 25.

Step by step solution

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 $z = 25$ .

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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

Short Answer

Step by step solution

Step 1. Understanding the concept of ratio.

Step 2. Simplifying the given equation.

Step 3. Solve the equations.

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In the figure, x:y=2:3and y:z=3:5If x=10 find the value of z.A 15B 20C 25D 30

Short Answer

Step by step solution

Step 1. Understanding the concept of ratio.

Step 2. Simplifying the given equation.

Step 3. Solve the equations.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Calculus

Discrete Mathematics

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

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