If 10% of X = 15% of Y = 1/5 of Z, then X : Y : Z is

The correct answer is Option (4) → 6 : 4 : 3

We are asked to find the ratio X : Y : Z given:

$10\% \text{ of } X = 15\% \text{ of } Y = \frac{1}{5} \text{ of } Z$

Step 1: Express as equations

Let this common value = k

$0.1 X = k \quad \Rightarrow \quad X = \frac{k}{0.1} = 10k$

$0.15 Y = k \quad \Rightarrow \quad Y = \frac{k}{0.15} = \frac{100k}{15} = \frac{20k}{3}$

$\frac{1}{5} Z = k \quad \Rightarrow \quad Z = 5k$

Step 2: Express all numbers as integers for ratio

• X = 10k
• Y = 20k/3 → multiply all by 3 to eliminate fraction:

$X : Y : Z = 10k : \frac{20k}{3} : 5k = 30 : 20 : 15$

Divide by 5:

$X : Y : Z = 6 : 4 : 3$