Two numbers are in the ratio $ 3:2 $. Their LCM and HCF are $ 24 $ and $ 4 $, respectively. The greater of the

Question

Two numbers are in the ratio $ 3:2 $. Their LCM and HCF are $ 24 $ and $ 4 $, respectively. The greater of the two numbers is:

Examoogle · Accepted Answer

The correct answer is Option C: 12. Since the numbers are $3x$ and $2x$, their HCF is $x$. Given HCF $= 4$, so $x=4$. The numbers are $3(4)=12$ and $2(4)=8$. The greater is $12$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Since the numbers are $3x$ and $2x$, their HCF is $x$. Given HCF $= 4$, so $x=4$. The numbers are $3(4)=12$ and $2(4)=8$. The greater is $12$.

Formula Used: $$LCM = HCF 	imes a 	imes b$$

Given: Ratio of two numbers = 3:2, LCM = 24, HCF = 4

Steps: Define the numbers: Since the ratio of the two numbers is $3:2$, let the numbers be $3x$ and $2x$, where $x$ is the HCF.. Use the given HCF: The problem states the HCF is $4$. Thus, $x = 4$.. Calculate the values: Substitute $x=4$ back into the expressions for the two numbers.. Identify the greater number: Comparing $12$ and $8$, the greater number is $12$.

Answer: C is correct because the numbers are $12$ and $8$, making $12$ the greater value.

Exam Tip: Always remember that any two numbers can be expressed as $H \cdot a$ and $H \cdot b$, where $H$ is the HCF and $a, b$ are co-prime integers forming the ratio.

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)