A man is engaged for planting trees for 10 hours. He plants 10 trees in an hour. He takes rest for 30 minutes after every hour. How many trees does he plant in 10 hours?

Options

A. 100
B. 50
C. 70
D. 45

Explanation

To solve the problem step by step, we will calculate how many trees the man can plant in 10 hours, considering his working hours and rest periods.

### Step 1: Determine the effective working time in 10 hours
The man works for 1 hour and then takes a rest of 30 minutes (which is 0.5 hours). Therefore, for every 1.5 hours, he works for 1 hour.

### Step 2: Calculate how many complete cycles fit into 10 hours
To find out how many complete cycles of 1.5 hours fit into 10 hours, we divide:
\[ \text{Number of cycles} = \frac{10 \text{ hours}}{1.5 \text{ hours/cycle}} = \frac{10}{1.5} \approx 6.67 \]
This means he can complete 6 full cycles, which accounts for 9 hours (6 cycles × 1.5 hours).

### Step 3: Calculate the total working hours in 6 cycles
In 6 cycles, he works for:
\[ \text{Total working hours} = 6 \text{ cycles} \times 1 \text{ hour/cycle} = 6 \text{ hours} \]

### Step 4: Calculate the number of trees planted in 6 hours
Since he plants 10 trees in 1 hour, in 6 hours, he plants:
\[ \text{Trees planted} = 6 \text{ hours} \times 10 \text{ trees/hour} = 60 \text{ trees} \]

### Step 5: Calculate the remaining time after 9 hours
After 9 hours (6 cycles), there is 1 hour left in the 10-hour period. In this remaining hour, he can work for another hour without needing to rest.

### Step 6: Calculate the trees planted in the remaining hour
In the last hour, he plants:
\[ \text{Trees planted in last hour} = 10 \text{ trees} \]

### Step 7: Calculate the total number of trees planted
Adding the trees planted in the 6 cycles and the last hour:
\[ \text{Total trees planted} = 60 \text{ trees} + 10 \text{ trees} = 70 \text{ trees} \]

### Final Answer
The total number of trees the man plants in 10 hours is **70 trees**.

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