Chapter 11: Q. 77 (page 774)

The ratio of a to b is $\frac{2}{3}$ . The sum of a and b is $10$ . What is the ratio of $a + b$ to $b - a$ ?

Short Answer

Expert verified

The ratio is $5$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$\frac{a}{b} = \frac{2}{3} . . . . . . (i) a + b = 10 . . . . . . (i i)$

Solve equation (ii) for a,

$a = 10 - b$

Substitute the value of a in equation (i),

$\frac{10 - b}{b} = \frac{2}{3} 30 - 3 b = 2 b b = 6$

Step 2. Find the value of a.

Substitute the value of bin equation (ii),

$a + 6 = 10 a = 4$

Then,

$b - a = 6 - 4 b - a = 2$

Therefore, the required ration is given below,

$\frac{a + b}{b - a} = \frac{10}{2} \frac{a + b}{b - a} = 5$

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The ratio of a to b is $\frac{2}{3}$ . The sum of a and b is $10$ . What is the ratio of $a + b$ to $b - a$ ?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the value of a.

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Step by step solution

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One App. One Place for Learning.

Most popular questions from this chapter

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The ratio of a to b is $\frac{2}{3}$ . The sum of a and b is $10$ . What is the ratio of $a + b$ to $b - a$ ?