If 177 is divided into 3 parts in the ratio `1/2: 2/3: 4/5`, then the second part is :

Options

A. 75
B. 45
C. 72
D. 60

Answer

To solve the problem of dividing 177 into three parts in the ratio \( \frac{1}{2} : \frac{2}{3} : \frac{4}{5} \), we can follow these steps:

### Step 1: Write the Ratios
We start by expressing the given ratios:
\[ \frac{1}{2} : \frac{2}{3} : \frac{4}{5} \]

### Step 2: Find the LCM of the Denominators
To make the ratios easier to work with, we need to find the least common multiple (LCM) of the denominators (2, 3, and 5).
- The LCM of 2, 3, and 5 is \( 30 \).

### Step 3: Convert the Ratios
Now, we will convert each part of the ratio to have a common denominator of 30:
\[ \frac{1}{2} \times 30 = 15, \quad \frac{2}{3} \times 30 = 20, \quad \frac{4}{5} \times 30 = 24 \]
Thus, the ratios become:
\[ 15 : 20 : 24 \]

### Step 4: Sum of the Parts
Next, we find the total parts represented by the ratios:
\[ 15 + 20 + 24 = 59 \]

### Step 5: Set Up the Equation
We know that these parts sum up to 177. Let \( p \) be the common multiplier for the ratios:
\[ 59p = 177 \]

### Step 6: Solve for \( p \)
Now, we solve for \( p \):
\[ p = \frac{177}{59} = 3 \]

### Step 7: Find the Second Part
The second part corresponds to \( 20p \):
\[ 20p = 20 \times 3 = 60 \]

Thus, the second part is:
\[ \boxed{60} \]

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