The three companies A, B, and C sold cars and bikes. The ratio of cars sold by A, B, and C is 4:5:6, respectively. The ratio of bikes sold by A, B, and C is 3:2:5, respectively. The difference between the number of cars and bikes sold by B is 18. Also, the ratio of cars sold by B to bikes sold by C is 8:11. What is the difference between the total cars sold by company C and the total bikes sold by company A?

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**Solution:**

1. Let the common multiplier for cars sold by A, B, and C be *x*. Then the cars sold are:
   - A: $4x$
   - B: $5x$
   - C: $6x$

2. Let the common multiplier for bikes sold by A, B, and C be *y*. Then the bikes sold are:
   - A: $3y$
   - B: $2y$
   - C: $5y$

3. Given that the difference between cars and bikes sold by B is 18:
   $$5x - 2y = 18$$

4. Also, the ratio of cars sold by B to bikes sold by C is 8:11:
   $$\frac{5x}{5y} = \frac{8}{11} \implies \frac{x}{y} = \frac{8}{11}$$

5. From the ratio, express *x* in terms of *y*:
   $$x = \frac{8}{11} y$$

6. Substitute into the difference equation:
   $$5 	imes \frac{8}{11} y - 2y = 18$$
   $$\frac{40}{11} y - 2y = 18$$
   $$\frac{40}{11} y - \frac{22}{11} y = 18$$
   $$\frac{18}{11} y = 18$$
   $$y = \frac{18 	imes 11}{18} = 11$$

7. Calculate *x*:
   $$x = \frac{8}{11} 	imes 11 = 8$$

8. Calculate cars sold by C:
   $$6x = 6 	imes 8 = 48$$

9. Calculate bikes sold by A:
   $$3y = 3 	imes 11 = 33$$

10. Find the difference between cars sold by C and bikes sold by A:
    $$48 - 33 = 15$$

**Answer:** 15

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