If 15% of X = 20% of Y, then X: Y is

Options

A. `3:4`
B. `4:3`
C. `17:16`
D. `16:17`

Answer

To solve the problem where 15% of X equals 20% of Y, we can follow these steps:

### Step 1: Write the equation based on the given percentages.
We start with the equation based on the information provided:
\[ 15\% \text{ of } X = 20\% \text{ of } Y \]
This can be expressed mathematically as:
\[ \frac{15}{100} \times X = \frac{20}{100} \times Y \]

### Step 2: Simplify the equation.
We can simplify the fractions:
\[ \frac{15}{100} = \frac{15 \div 5}{100 \div 5} = \frac{3}{20} \]
\[ \frac{20}{100} = \frac{20 \div 20}{100 \div 20} = \frac{1}{5} \]
So, we rewrite the equation as:
\[ \frac{3}{20} X = \frac{1}{5} Y \]

### Step 3: Eliminate the fractions.
To eliminate the fractions, we can multiply both sides of the equation by 20 (the least common multiple of the denominators):
\[ 20 \times \frac{3}{20} X = 20 \times \frac{1}{5} Y \]
This simplifies to:
\[ 3X = 4Y \]

### Step 4: Rearrange the equation to find the ratio.
Now, we can rearrange the equation to express the ratio of X to Y:
\[ \frac{X}{Y} = \frac{4}{3} \]

### Step 5: Write the final answer.
Thus, the ratio of X to Y is:
\[ X : Y = 4 : 3 \]

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