Speed of a boat in still water is 20 km/hr and speed of current 'is 4 km/hr, if time taken by boat' to cover a distance of (d-40) km upstream is one hour more than the time taken by boat to cover a distance of (d - 24) km in downstream, then find time taken by boat to cover a distance of (d +48) km in downstream and in upstream both?

Options

A. A)16.5 hours
B. B)17 hours
C. C)18 hours
D. D)17.5 hours

Answer

To solve the problem step by step, we will first identify the speeds and then set up the equations based on the information given.

### Given:
- Speed of the boat in still water = 20 km/hr
- Speed of the current = 4 km/hr
- Speed of the boat upstream = Speed of the boat - Speed of the current = 20 - 4 = 16 km/hr
- Speed of the boat downstream = Speed of the boat + Speed of the current = 20 + 4 = 24 km/hr

### Step 1: Set up the equation for upstream and downstream
Let \( d \) be the distance in km.

- Distance covered upstream = \( d - 40 \) km
- Distance covered downstream = \( d - 24 \) km

The time taken to cover a distance is given by the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

**Time taken upstream:**
\[ \text{Time}_{up} = \frac{d - 40}{16} \]

**Time taken downstream:**
\[ \text{Time}_{down} = \frac{d - 24}{24} \]

According to the problem, the time taken upstream is 1 hour more than the time taken downstream:
\[ \frac{d - 40}{16} = \frac{d - 24}{24} + 1 \]

### Step 2: Solve the equation
Now, we will solve the equation:
1. Multiply through by 48 (the LCM of 16 and 24) to eliminate the denominators:
\[ 48 \left(\frac{d - 40}{16}\right) = 48 \left(\frac{d - 24}{24} + 1\right) \]

2. This simplifies to:
\[ 3(d - 40) = 2(d - 24) + 48 \]

3. Expanding both sides:
\[ 3d - 120 = 2d - 48 + 48 \]
\[ 3d - 120 = 2d \]

4. Rearranging gives:
\[ 3d - 2d = 120 \]
\[ d = 120 \text{ km} \]

### Step 3: Calculate time taken to cover \( d + 48 \) km
Now we need to find the time taken to cover \( d + 48 \) km in both upstream and downstream.

1. Calculate \( d + 48 \):
\[ d + 48 = 120 + 48 = 168 \text{ km} \]

2. **Time taken downstream**:
\[ \text{Time}_{down} = \frac{168}{24} = 7 \text{ hours} \]

3. **Time taken upstream**:
\[ \text{Time}_{up} = \frac{168}{16} = 10.5 \text{ hours} \]

### Step 4: Total time taken
Now, we add the times taken upstream and downstream:
\[ \text{Total time} = \text{Time}_{up} + \text{Time}_{down} = 10.5 + 7 = 17.5 \text{ hours} \]

### Final Answer:
The total time taken by the boat to cover a distance of \( d + 48 \) km in both upstream and downstream is **17.5 hours**.