If $\frac{3}(10}$ part of a pipe is in mud, $\frac{3}{5}$ part in water and remaining 5 metre above the water surface, then the length of the pipe will be :

Question

Accepted Answer

To determine the total length of the pipe, we need to consider the parts of the pipe that are in mud, in water, and above the water surface.

1. **Part in Mud**: According to the problem, $\frac{3}{10}$ of the pipe is in mud.

2. **Part in Water**: $\frac{3}{5}$ of the pipe is in water.

3. **Part Above Water**: The remaining part of the pipe, which is above the water surface, is given as 5 meters.

To find the total length of the pipe, we need to add these parts together. Let's denote the total length of the pipe as $L$.

- The part in mud is $\frac{3}{10}L$.
- The part in water is $\frac{3}{5}L$.
- The part above water is 5 meters.

The sum of these parts should equal the total length of the pipe:

$$
\frac{3}{10}L + \frac{3}{5}L + 5 = L
$$

To solve this equation, we first need a common denominator for the fractions, which is 10:

$$
\frac{3}{10}L + \frac{6}{10}L + 5 = L
$$

Combine the fractions:

$$
\frac{9}{10}L + 5 = L
$$

Subtract $\frac{9}{10}L$ from both sides:

$$
5 = L - \frac{9}{10}L
$$

$$
5 = \frac{1}{10}L
$$

Multiply both sides by 10 to solve for $L$:

$$
L = 50
$$

Thus, the total length of the pipe is 50 meters, which corresponds to Option 4.

**Explanation for Incorrect Options:**

1. **Option 1 (15 m)**: This option is incorrect because if the total length were 15 meters, the part above water (5 meters) would not fit the fractions given for the parts in mud and water.

2. **Option 2 (60 m)**: This option is incorrect because solving the equation with 60 meters would not satisfy the condition that 5 meters is above the water surface.

3. **Option 3 (30 m)**: This option is incorrect because, similar to Option 1, the fractions of the pipe in mud and water would not leave 5 meters above the water surface.

Therefore, the correct answer is Option 4, which is 50 meters.