A man covers a distance of 1200 km in 70 days resting 9 hours a day, if he rests 10 hours a day and walks with speed `1 1/2` times of the previous in how many days will he cover 840 km ?

Options

A. A) 39 days
B. B) 37 days
C. C) 35 days
D. D) 33 days

Answer

To solve the problem step by step, we need to determine the time it will take for the man to cover 840 km given the new conditions.

### Step 1: Calculate the initial speed
The man covers a distance of 1200 km in 70 days, resting 9 hours a day.

1. Total hours in 70 days = 70 days × 24 hours/day = 1680 hours.
2. Total resting hours = 9 hours/day × 70 days = 630 hours.
3. Total walking hours = Total hours - Total resting hours = 1680 hours - 630 hours = 1050 hours.

Now, we can calculate the speed:
- Speed = Distance / Time = 1200 km / 1050 hours = 8/7 km/h.

### Step 2: Calculate the new speed
The man will now rest for 10 hours a day instead of 9 hours, and his speed will be 1.5 times the previous speed.

1. New speed = 1.5 × (8/7 km/h) = (3/2) × (8/7) = 12/7 km/h.

### Step 3: Calculate the time to cover 840 km at the new speed
Now, we need to find out how long it will take to cover 840 km with the new speed.

1. Time = Distance / Speed = 840 km / (12/7 km/h) = 840 × (7/12) = 490 hours.

### Step 4: Calculate the effective walking hours per day
The man now rests for 10 hours a day, so the walking hours per day will be:

1. Walking hours per day = 24 hours - 10 hours = 14 hours.

### Step 5: Calculate the number of days to cover 840 km
Finally, we can find out how many days it will take to cover 840 km.

1. Number of days = Total time / Walking hours per day = 490 hours / 14 hours/day = 35 days.

### Final Answer
Therefore, the man will take **35 days** to cover 840 km under the new conditions.

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