Question

If $3x = 4y = 12z$, what is the ratio $x:y:z$?

• A. 4:3:1
• B. 3:4:1
• C. 4:3:2
• D. 3:4:2

Hint:

Equate expressions to a common variable and simplify to find ratios.

Answer 1

The Correct Option is A

- Step 1: Let $3x = 4y = 12z = k$.
- Step 2: Then, $x = \frac{k}{3}$, $y = \frac{k}{4}$, $z = \frac{k}{12}$.
- Step 3: Ratio $x:y:z = \frac{k}{3} : \frac{k}{4} : \frac{k}{12} = \frac{1}{3} : \frac{1}{4} : \frac{1}{12}$.
- Step 4: Multiply by 12 to get whole numbers: $4:3:1$.
- Step 5: Verify: If $x = 4t$, $y = 3t$, $z = t$, then $3x = 12t$, $4y = 12t$, $12z = 12t$, equal.
- Step 6: Option (1) is 4:3:1, correct.