**The ratio of speed of boat in still water to speed of stream is 8 : 1. It takes 4 hours by boat to cover 54 km downstream and 42 km upstream. Find the downstream speed of the boat.**

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**Solution:**

1. Let the speed of the boat in still water be $8x$ kmph and the speed of the stream be $x$ kmph (given ratio 8:1).

2. Then,
   - Downstream speed = $8x + x = 9x$ kmph
   - Upstream speed = $8x - x = 7x$ kmph

3. Given that the total time taken to cover 54 km downstream and 42 km upstream is 4 hours:
   $$\frac{54}{9x} + \frac{42}{7x} = 4$$

4. Simplify the equation:
   $$\frac{54}{9x} = \frac{6}{x} \quad 	ext{and} \quad \frac{42}{7x} = \frac{6}{x}$$

So,
   $$\frac{6}{x} + \frac{6}{x} = 4$$
   $$\frac{12}{x} = 4$$

5. Solve for $x$:
   $$x = \frac{12}{4} = 3$$

6. Calculate downstream speed:
   $$9x = 9 	imes 3 = 27 	ext{ kmph}$$

**Answer:** $27 	ext{ kmph}$

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