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If overset(1)A:overset(1)B:overset(1)C=2...

If `overset(1)A:overset(1)B:overset(1)C=2:3:4`, then what is the ratio of `A:B:C` ?

A

`6 : 4 : 3`

B

`4 : 3 : 6`

C

`3 : 6 : 4`

D

`12 : 6 : 8`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we start with the given ratio: \[ \frac{1}{A} : \frac{1}{B} : \frac{1}{C} = 2 : 3 : 4 \] ### Step 1: Understand the given ratio This means that the reciprocals of A, B, and C are in the ratio of 2:3:4. ### Step 2: Express the ratios in terms of a common variable Let’s denote the common variable for the ratios as \( k \). Therefore, we can write: \[ \frac{1}{A} = 2k, \quad \frac{1}{B} = 3k, \quad \frac{1}{C} = 4k \] ### Step 3: Find A, B, and C in terms of k Now, we can find A, B, and C by taking the reciprocals: \[ A = \frac{1}{2k}, \quad B = \frac{1}{3k}, \quad C = \frac{1}{4k} \] ### Step 4: Find a common denominator To find the ratio \( A:B:C \), we need to express A, B, and C with a common denominator. The least common multiple (LCM) of the denominators (2, 3, and 4) is 12. ### Step 5: Rewrite A, B, and C using the LCM Now we can rewrite A, B, and C: \[ A = \frac{1}{2k} = \frac{6}{12k}, \quad B = \frac{1}{3k} = \frac{4}{12k}, \quad C = \frac{1}{4k} = \frac{3}{12k} \] ### Step 6: Write the ratio A:B:C Thus, the ratio of A:B:C can be expressed as: \[ A:B:C = 6:4:3 \] ### Conclusion The final ratio of A:B:C is: \[ \text{A:B:C} = 6:4:3 \]
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