If 10% of X = 15% of Y = 1/5 of Z, then X: Y: Z is Option 1: 6 : 3 : 4 Option 2: 10 : 15 : 18 Option 3: 15 : 10 : 18 Option 4: 6 : 4 : 3

Answer: 6 : 4 : 3. Solution: Given that 10% of X = 15% of Y = 1/5 of Z. Converting to fractions: 10/100 x X = X/10 15/100 x Y = 3Y/20 1/5 x Z = Z/5 Therefore: X/10 = 3Y/20 = Z/5 Let each expression equal k: X/10 = k 3Y/20 = k Z/5 = k Solving for X, Y, and Z: X/10 = k X = 10k 3Y/20 = k 3Y = 20k Y = 20k/3 Z/5 = k Z = 5k The ratio is: X : Y : Z = 10k : 20k/3 : 5k Multiplying by 3 to eliminate the fraction: X : Y : Z = 30k : 20k : 15k X : Y : Z = 30 : 20 : 15 Dividing by the common factor 5: 30 5 = 6 20 5 = 4 15 5 = 3 Therefore, X : Y : Z = 6 : 4 : 3

Arithmetic

Ratio, Proportion & Variation

Medium

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

6 : 3 : 4

10 : 15 : 18

15 : 10 : 18

6 : 4 : 3

✅ Correct Option: 4

Given that 10% of $X$ = 15% of $Y$ = $\frac{1}{5}$ of $Z$ .

Converting to fractions:

$\frac{10}{100} \times X = \frac{X}{10}$

$\frac{15}{100} \times Y = \frac{3Y}{20}$

$\frac{1}{5} \times Z = \frac{Z}{5}$

Therefore:

$\frac{X}{10} = \frac{3Y}{20} = \frac{Z}{5}$

Let each expression equal $k$ :

$\frac{X}{10} = k$

$\frac{3Y}{20} = k$

$\frac{Z}{5} = k$

Solving for $X$ , $Y$ , and $Z$ :

$\frac{X}{10} = k$

$X = 10k$

$\frac{3Y}{20} = k$

$3Y = 20k$

$Y = \frac{20k}{3}$

$\frac{Z}{5} = k$

$Z = 5k$

The ratio is:

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

Multiplying by 3 to eliminate the fraction:

$X : Y : Z = 30k : 20k : 15k$

$X : Y : Z = 30 : 20 : 15$

Dividing by the common factor 5:

$30 \div 5 = 6$

$20 \div 5 = 4$

$15 \div 5 = 3$

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

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

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