Question

the mean proportional of a and b is 10 and the value of a is 4 times the value of b. the value of a + b (a>0,b>0) is
(a)20 (b)25 (c)10 (d)29​

Answer 1

$\textsf{\large{\underline{Solution}:}}$

Given that: Mean proportional of a and b is 10.

Therefore:

$\rm \longmapsto \sqrt{ab} = 10$

$\rm \longmapsto ab = 100$

Now, a is 4 times the value of b. Therefore:

$\rm \longmapsto (4b)b = 100$

$\rm \longmapsto 4 {b}^{2} = 100$

$\rm \longmapsto {b}^{2} = 25$

$\rm \longmapsto b = 5 \: \: \: \: (as \: b > 0)$

Therefore, the value of a + b will be:

$\rm = a + b$

$\rm = 4b + b$

$\rm = 5b$

$\rm = 5 \times 5$

$\rm = 25$

★ Which is our required answer.

$\textsf{\large{\underline{Learn More}:}}$

A. If a : b and c : d are two ratios such that a : b : : c : d. Then the following results hold true.

1. Invertendo.

$\rm\longrightarrow b : a : : d : c$

2. Alternendo.

$\rm\longrightarrow a : c : : b : d$

3. Componendo.

$\rm\longrightarrow (a + b) : b: : (c + d) : d$

4. Dividendo.

$\rm\longrightarrow (a - b) : b: : (c - d) : d$

5. Componendo and dividendo.

$\rm\longrightarrow (a + b) : (a - b): : (c + d) :(c - d)$

6. Convertendo.

$\rm\longrightarrow a : (a - b): :c:(c - d)$

B. If a, b and c are in continued proportion, then –

→ a/b = b/c

→ b² = ac