If `L:M= 3:5 and M:N= 2:3`, then `N:L = ? `

Options

A. A)`2:1`
B. B)`5:2`
C. C)`3:2`
D. D)`1:2`

Answer

To find the ratio \( N:L \) given the ratios \( L:M = 3:5 \) and \( M:N = 2:3 \), we can follow these steps:

### Step 1: Express the ratios in terms of a common variable
From the first ratio \( L:M = 3:5 \), we can express \( L \) and \( M \) as:
- \( L = 3x \)
- \( M = 5x \)

From the second ratio \( M:N = 2:3 \), we can express \( M \) and \( N \) as:
- \( M = 2y \)
- \( N = 3y \)

### Step 2: Set the expressions for \( M \) equal to each other
Since both expressions represent \( M \), we can set them equal:
\[ 5x = 2y \]

### Step 3: Solve for one variable in terms of the other
From the equation \( 5x = 2y \), we can express \( y \) in terms of \( x \):
\[ y = \frac{5x}{2} \]

### Step 4: Substitute \( y \) back into the expression for \( N \)
Now we can substitute \( y \) into the expression for \( N \):
\[ N = 3y = 3 \left(\frac{5x}{2}\right) = \frac{15x}{2} \]

### Step 5: Write the ratio \( N:L \)
Now we have:
- \( N = \frac{15x}{2} \)
- \( L = 3x \)

To find the ratio \( N:L \):
\[ N:L = \frac{15x/2}{3x} \]

### Step 6: Simplify the ratio
When we simplify \( \frac{15x/2}{3x} \):
\[ N:L = \frac{15}{2 \cdot 3} = \frac{15}{6} = \frac{5}{2} \]

### Final Answer
Thus, the ratio \( N:L \) is \( 5:2 \).

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