Working 15 hours a day, Goldy can complete a piece of work in 24 days. How many hours a day he should work so as to finish the work in 18 days?

Options

A. 20
B. 16
C. 18
D. 8

Answer

To solve the problem step by step, we will use the relationship between the number of hours worked per day, the number of days, and the total work done.

### Step 1: Understand the given data
Goldy works for 15 hours a day and completes the work in 24 days. We need to find out how many hours he should work per day (let's call this T2) to finish the same work in 18 days.

### Step 2: Calculate total work done in the first scenario
Total work can be calculated as:
\[ \text{Total Work} = \text{Hours per day} \times \text{Number of days} \]
So, in the first scenario:
\[ \text{Total Work} = 15 \text{ hours/day} \times 24 \text{ days} = 360 \text{ hours} \]

### Step 3: Set up the equation for the second scenario
In the second scenario, Goldy needs to finish the same total work (360 hours) in 18 days. We can express this as:
\[ \text{Total Work} = T2 \times D2 \]
Where D2 is the number of days in the second scenario (18 days). Therefore:
\[ 360 = T2 \times 18 \]

### Step 4: Solve for T2
To find T2, we rearrange the equation:
\[ T2 = \frac{360}{18} \]
Calculating this gives:
\[ T2 = 20 \text{ hours/day} \]

### Conclusion
Goldy should work for **20 hours a day** to finish the work in 18 days.

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