Raju has to cover a distance of 240 km in 4 hours. If he covers one-third of the journey in `2/7th` time , what is his speed at the beginning of the journey ?

Options

A. 70 km/hr
B. 75 km/hr
C. 60 km/hr
D. 65 km/hr

Answer

To solve the problem step by step, we need to find Raju's speed at the beginning of his journey. Here’s how we can do it:

### Step 1: Determine the total distance and the fraction of the journey covered.
Raju has to cover a total distance of 240 km. He covers one-third of this distance.

**Calculation:**
\[ \text{Distance covered} = \frac{1}{3} \times 240 \text{ km} = 80 \text{ km} \]

**Hint:** To find one-third of a distance, multiply the total distance by \( \frac{1}{3} \).

### Step 2: Calculate the time taken to cover this distance.
The total time for the journey is 4 hours. Raju covers one-third of the journey in \( \frac{2}{7} \) of the total time.

**Calculation:**
\[ \text{Time taken} = \frac{2}{7} \times 4 \text{ hours} = \frac{8}{7} \text{ hours} \]

**Hint:** To find a fraction of a time, multiply the total time by that fraction.

### Step 3: Calculate Raju's speed during this time.
Speed is calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

**Calculation:**
\[ \text{Speed} = \frac{80 \text{ km}}{\frac{8}{7} \text{ hours}} = 80 \times \frac{7}{8} = 70 \text{ km/h} \]

**Hint:** When dividing by a fraction, multiply by its reciprocal.

### Final Answer:
Raju's speed at the beginning of the journey is **70 km/h**.