The pie charts represent the distances covered by a boat moving upstream and downstream over seven days of a week. The total distance covered upstream is $1800 ext{ km}$ and downstream is $1500 ext{ km}$. The percentages of distances covered each day are as follows:

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1756842413/aptidude_questions/t4atmcpexa0eqnn6gtdx.png)

The table below shows the speed of the stream (in km/hr) on different days:

| Day | Speed of Stream (km/hr) |
|-----------|-------------------------|
| Monday | 2 |
| Tuesday | 3 |
| Wednesday | - |
| Thursday | 1 |
| Friday | 2 |
| Saturday | - |
| Sunday | 4 |

If the time taken by the boat to travel upstream on Thursday is equal to the time taken to travel downstream on Monday, and the speed of the boat in still water on Monday is $16 ext{ kmph}$, find the speed of the boat in still water on Thursday.

Question

The pie charts represent the distances covered by a boat moving upstream and downstream over seven days of a week. The total distance covered upstream is $1800 	ext{ km}$ and downstream is $1500 	ext{ km}$. The percentages of distances covered each day are as follows:

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1756842413/aptidude_questions/t4atmcpexa0eqnn6gtdx.png)

The table below shows the speed of the stream (in km/hr) on different days:

| Day       | Speed of Stream (km/hr) |
|-----------|-------------------------|
| Monday    | 2                       |
| Tuesday   | 3                       |
| Wednesday | -                       |
| Thursday  | 1                       |
| Friday    | 2                       |
| Saturday  | -                       |
| Sunday    | 4                       |

If the time taken by the boat to travel upstream on Thursday is equal to the time taken to travel downstream on Monday, and the speed of the boat in still water on Monday is $16 	ext{ kmph}$, find the speed of the boat in still water on Thursday.

Accepted Answer

**Solution:**

1. **Calculate the distances traveled upstream on Thursday and downstream on Monday:**
   - Upstream distance on Thursday = 12% of 1800 km = $0.12 	imes 1800 = 216 	ext{ km}$
   - Downstream distance on Monday = 16% of 1500 km = $0.16 	imes 1500 = 240 	ext{ km}$

2. **Given:**
   - Speed of stream on Monday = $2 	ext{ km/hr}$
   - Speed of stream on Thursday = $1 	ext{ km/hr}$
   - Speed of boat in still water on Monday = $16 	ext{ km/hr}$

3. **Calculate the speed of boat upstream and downstream on Monday:**
   - Upstream speed on Monday = speed of boat in still water - speed of stream = $16 - 2 = 14 	ext{ km/hr}$
   - Downstream speed on Monday = speed of boat in still water + speed of stream = $16 + 2 = 18 	ext{ km/hr}$

4. **Calculate the time taken to travel downstream on Monday:**
   $$	ext{Time} = \frac{	ext{Distance}}{	ext{Speed}} = \frac{240}{18} = \frac{40}{3} 	ext{ hours} \approx 13.33 	ext{ hours}$$

5. **Let the speed of boat in still water on Thursday be $x$ km/hr.**
   - Upstream speed on Thursday = $x - 1$ (since stream speed on Thursday is 1 km/hr)

6. **Time taken to travel upstream on Thursday is equal to time taken downstream on Monday:**
   $$\frac{216}{x - 1} = \frac{40}{3}$$

7. **Solve for $x$:**
   $$216 = \frac{40}{3} (x - 1)$$
   $$216 = \frac{40}{3} x - \frac{40}{3}$$
   Multiply both sides by 3:
   $$648 = 40x - 40$$
   $$40x = 648 + 40 = 688$$
   $$x = \frac{688}{40} = 17.2 	ext{ km/hr}$$

**Answer:** $17.2 	ext{ kmph}$

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