If $ a : b = 3 : 2 $ and $ b : c = 3 : 2 $, then $ a : b : c = ? $

Question

Examoogle · Accepted Answer

The correct answer is Option A: $9 : 6 : 4$. To find $a : b : c$ when $a : b$ and $b : c$ are given, align the common term $b$ by taking the LCM of its two values (2 and 3, which is 6) and multiply both ratios accordingly.

Step-by-Step Solution & Concepts:
Shortcut Trick: To find $a : b : c$ when $a : b$ and $b : c$ are given, align the common term $b$ by taking the LCM of its two values (2 and 3, which is 6) and multiply both ratios accordingly.

Formula Used: $$a : b : c = (a 	imes b_2) : (b_1 	imes b_2) : (b_1 	imes c)$$

Given: $a : b = 3 : 2$ and $b : c = 3 : 2$

Steps: Write the given ratios: We are given two ratios involving three variables $a$, $b$, and $c$: $a : b = 3 : 2$ and $b : c = 3 : 2$.. Equate the common term ($b$): The value of $b$ in the first ratio is $2$, and in the second ratio, it is $3$. To make $b$ equal, find the LCM of $2$ and $3$, which is $6$.. Scale both ratios: Multiply the first ratio ($3:2$) by $3$ to get $9:6$, and multiply the second ratio ($3:2$) by $2$ to get $6:4$.. Combine into a single ratio: Combining both scaled ratios yields $a : b : c = 9 : 6 : 4$.

Answer: A is correct because combining the ratios $a : b = 3 : 2$ and $b : c = 3 : 2$ by making the common term $b$ equal results in $9 : 6 : 4$.

Exam Tip: Proportion and ratio-scaling techniques are frequently used in partnership problems, mixture and allegation, and physics numericals involving proportional quantities.

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