A painter can paint a fence in 24 hours. After 6 hours he takes a break. What fraction of the fence is yet to be painted ?

Options

A. 0.6
B. 0.2
C. 0.75
D. 0.8

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Determine the rate of work of the painter.
The painter can complete the entire fence in 24 hours. Therefore, the rate of work per hour is:
\[ \text{Rate of work} = \frac{1 \text{ fence}}{24 \text{ hours}} = \frac{1}{24} \text{ fences per hour} \]

**Hint:** To find the rate of work, divide the total work (1 fence) by the total time taken (24 hours).

### Step 2: Calculate the amount of work done in 6 hours.
In 6 hours, the amount of work done by the painter is:
\[ \text{Work done} = \text{Rate of work} \times \text{Time worked} = \frac{1}{24} \times 6 = \frac{6}{24} = \frac{1}{4} \text{ of the fence} \]

**Hint:** Multiply the rate of work by the number of hours worked to find the total work completed.

### Step 3: Determine the remaining work.
Since the total work is 1 fence and the painter has completed \(\frac{1}{4}\) of it, the remaining work is:
\[ \text{Remaining work} = 1 - \text{Work done} = 1 - \frac{1}{4} = \frac{3}{4} \text{ of the fence} \]

**Hint:** To find the remaining work, subtract the work done from the total work (1 fence).

### Final Answer:
The fraction of the fence that is yet to be painted is \(\frac{3}{4}\).

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