If $ a : b = 3 : 4 $ and $ b : c = 4 : 1 $, then $ a : b : c = ? $

Question

Examoogle · Accepted Answer

The correct answer is Option C: 4 : 1. Since the common term '$b$' has the same value ($4$) in both ratios ($a : b = 3 : 4$ and $b : c = 4 : 1$), you can directly combine them as $3 : 4 : 1$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Since the common term '$b$' has the same value ($4$) in both ratios ($a : b = 3 : 4$ and $b : c = 4 : 1$), you can directly combine them as $3 : 4 : 1$.

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

Given: a : b = 3 : 4 and b : c = 4 : 1

Steps: Step 1: Write down the given ratios: We are given two individual ratios: $a : b = 3 : 4$ and $b : c = 4 : 1$.. Step 2: Check the common term: The common term in both ratios is $b$. In the first ratio, $b = 4$, and in the second ratio, $b = 4$.. Step 3: Combine the ratios: Since the value of the common term $b$ is identical in both ratios, we can directly write the combined ratio $a : b : c$ as $3 : 4 : 1$.

Answer: C is correct because combining the given ratios $a : b = 3 : 4$ and $b : c = 4 : 1$ directly yields $3 : 4 : 1$ since the common term $b$ is already equal to $4$.

Exam Tip: This fundamental ratio-combining technique is widely used in partnership, mixture, and alligation problems in quantitative aptitude.

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