Chapter 11: Q. 78 (page 774)

The ratio of a to b is $4 : 3$ . The sum of a and b is $14$ . What is the ratio of $a - b$ to $a + b$ ?

Short Answer

Expert verified

The ratio is $\frac{1}{7}$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$\frac{a}{b} = \frac{4}{3} . . . . . . (i) a + b = 14 . . . . . . (i i)$

Solve equation (ii) for a,

$a = 14 - b$

Substitute the value of a in equation (i),

$\frac{14 - b}{b} = \frac{4}{3} 42 - 3 b = 4 b 42 = 7 b b = 6$

Step 2. Find the value of a.

Substitute the value of bin equation (ii),

$a + 6 = 14 a = 8$

Then,

$a - b = 8 - 6 a - b = 2$

Therefore, the required ration is given below,

$\frac{a - b}{a + b} = \frac{2}{14} \frac{a - b}{a + b} = \frac{1}{7}$

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The ratio of a to b is $4 : 3$ . The sum of a and b is $14$ . What is the ratio of $a - b$ to $a + b$ ?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the value of a.

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The ratio of a to b is 4:3. The sum of a and b is 14. What is the ratio of a-b to a+b?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the value of a.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

The ratio of a to b is $4 : 3$ . The sum of a and b is $14$ . What is the ratio of $a - b$ to $a + b$ ?