A pole is cut into two pieces in the ratio `8: 9`. If the total length is 1615 m, then find the length of smaller part.

Options

A. 420 m
B. 670 m
C. 760 m
D. 940 m

Answer

To solve the problem of finding the length of the smaller part of the pole that is cut into two pieces in the ratio of 8:9, follow these steps:

### Step 1: Understand the Ratio
The ratio of the two parts is given as 8:9. This means that for every 8 parts of the first piece, there are 9 parts of the second piece.

### Step 2: Calculate the Total Parts
To find the total number of parts, we add the parts of both pieces together:
\[ \text{Total parts} = 8 + 9 = 17 \]

### Step 3: Determine the Length of Each Part
The total length of the pole is given as 1615 meters. To find the length of one part, we divide the total length by the total number of parts:
\[ \text{Length of one part} = \frac{1615}{17} = 95 \text{ meters} \]

### Step 4: Calculate the Length of the Smaller Part
Since the smaller part corresponds to the ratio of 8 parts, we can find its length by multiplying the length of one part by 8:
\[ \text{Length of smaller part} = 8 \times 95 = 760 \text{ meters} \]

### Final Answer
The length of the smaller part of the pole is **760 meters**.

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