Comparing Quantities: A:B:C

To solve the given problem, we have the equation 3A = 2B = 4C. We need to find the ratio of A, B, and C, which is represented as A:B:C. Let's break down the problem into smaller steps to find the solution.

Step 1: Understanding the equation
The equation 3A = 2B = 4C implies that the values of 3A, 2B, and 4C are equal. This means that the ratios of A to B, B to C, and A to C are also equal. We can represent these ratios as A/B, B/C, and A/C.

Step 2: Finding the ratio A:B:C
To find the ratio A:B:C, we need to convert the equation 3A = 2B = 4C into a form where we have A, B, and C on one side and numerical constants on the other side. Let's do this by solving the equation for A, B, and C.

Since 3A = 2B, we can write A = (2/3)B.
Similarly, since 2B = 4C, we can write B = (4/2)C = 2C.

Now, we have A = (2/3)B = (2/3)(2C) = (4/3)C.

Step 3: Simplifying the ratios
We have A = (4/3)C and B = 2C. Let's substitute these values into the ratios A/B, B/C, and A/C to simplify them.

A/B = ((4/3)C)/(2C) = 2/3
B/C = (2C)/C = 2
A/C = ((4/3)C)/C = 4/3

Therefore, the simplified ratio A:B:C is 2/3 : 2 : 4/3.

Step 4: Final answer
We can multiply the above ratios by a common factor to simplify them further. Let's multiply all the ratios by 3 to eliminate the fractions.

2/3 : 2 : 4/3
(2/3) * 3 : 2 * 3 : (4/3) * 3
2 : 6 : 4

Therefore, the final ratio A:B:C is 2 : 6 : 4.

Summary:
To summarize, given the equation 3A = 2B = 4C, we found the ratio A:B:C by solving the equation for A, B, and C. The final ratio is 2 : 6 : 4.

Let the 3A=2B=4C=K
then 3A=K
A=K/3

and 2B=K
B=K/2

and 4C=K
C=K/4

So,
A:B:C = K/3:K/2:K/4
=1/3:1/2:1/4

So LCM of 3 & 4 is = 12

A:B:C = 1/3*4/4 : 1/2*6/6 : 1/4*3/3
= 4/12 : 6/12 : 3/12
= 4:6:3