A man can reach a certain place in 30 hours. If he reduces his speed by `(1)/(15)th`, he goes 10km less in that time. Find his speed per hour.

Options

A. 6km/hr
B. `5(1)/(2)` km/hr
C. 4km/hr
D. 5km/hr

Answer

To solve the problem step by step, we will use the relationship between speed, distance, and time.

### Step 1: Define the variables
Let the speed of the man be \( S \) km/h.

### Step 2: Calculate the distance
The distance he travels in 30 hours at speed \( S \) is given by:
\[ \text{Distance} = \text{Speed} \times \text{Time} = S \times 30 = 30S \text{ km} \]

### Step 3: Determine the new speed
If he reduces his speed by \( \frac{1}{15} \) of his speed, his new speed becomes:
\[ \text{New Speed} = S - \frac{S}{15} = S \left(1 - \frac{1}{15}\right) = S \left(\frac{14}{15}\right) = \frac{14S}{15} \text{ km/h} \]

### Step 4: Calculate the distance at the new speed
At the new speed, he still takes 30 hours to travel, but now he travels 10 km less:
\[ \text{New Distance} = \text{New Speed} \times \text{Time} = \left(\frac{14S}{15}\right) \times 30 = \frac{14S \times 30}{15} = 28S \text{ km} \]

### Step 5: Set up the equation
According to the problem, the new distance is 10 km less than the original distance:
\[ 28S = 30S - 10 \]

### Step 6: Solve for \( S \)
Rearranging the equation gives:
\[ 30S - 28S = 10 \\ 2S = 10 \\ S = \frac{10}{2} = 5 \text{ km/h} \]

### Final Answer
The speed of the man is \( 5 \) km/h.

---