Question

The quantities a, 6, 12, and b are in continued proportion. Find the values of a and b.

Continued proportion means a:b :: b:c :: c:d

• A. 3 and 24
• B. 2 and 15
• C. 4 and 45
• D. 5 and 25

Answer 1

The correct option is A

3 and 24

Continued proportion means a:b :: b:c :: c:d

So, when the quantities are in continued proportion, then,
$\frac{a}{6}=\frac{6}{12}=\frac{12}{b}$

From this, we have $\frac{a}{6}=\frac{6}{12}$
a = $\frac{36}{12}$ = 3.

We also have $\frac{6}{12}=\frac{12}{b}$
b = $\frac{12\times 12}{6}$
b = 24

Hence the values of a and b are 3 and 24 respectively.