40% of a number is equal to three fourth's of another number. What is the ratio between the first number and the second number ?

Options

A. 15 : 8
B. 12 : 19
C. 14 : 17
D. can't be determined

Answer

To solve the problem step by step, we will follow the reasoning presented in the video transcript.

### Step 1: Understand the problem
We are given that 40% of a number (let's call it \( n_1 \)) is equal to three-fourths of another number (let's call it \( n_2 \)).

### Step 2: Convert percentages and fractions
First, we need to convert 40% into a fraction.
- 40% can be expressed as \( \frac{40}{100} = \frac{2}{5} \).

### Step 3: Set up the equation
According to the problem, we can write the equation:
\[ \frac{2}{5} n_1 = \frac{3}{4} n_2 \]

### Step 4: Rearranging the equation
To find the ratio \( \frac{n_1}{n_2} \), we can rearrange the equation:
\[ n_1 = \frac{3}{4} n_2 \cdot \frac{5}{2} \]

### Step 5: Simplifying the equation
Now, we simplify the right-hand side:
\[ n_1 = \frac{3 \cdot 5}{4 \cdot 2} n_2 \]
\[ n_1 = \frac{15}{8} n_2 \]

### Step 6: Finding the ratio
From the equation \( n_1 = \frac{15}{8} n_2 \), we can express the ratio \( \frac{n_1}{n_2} \):
\[ \frac{n_1}{n_2} = \frac{15}{8} \]

### Step 7: Expressing the ratio in standard form
The ratio \( n_1 : n_2 \) can be written as:
\[ n_1 : n_2 = 15 : 8 \]

### Conclusion
Thus, the ratio between the first number and the second number is \( 15 : 8 \).

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