The price of a book is thrice that of an exercise book. If a student spent #9600 on books and at 8000 on exercise books he has 86 items altogether. a) find the price of an exercise book. b) What is the difference between the price?

Let $P_b$ be the price of one book and $P_e$ be the price of one exercise book.
Let $N_b$ be the number of books and $N_e$ be the number of exercise books.

From the problem statement, we have the following relationships:

1. The price of a book is thrice that of an exercise book: $$P_b = 3 P_e$$
2. A student spent N9600 on books: $$N_b P_b = 9600$$
3. A student spent N8000 on exercise books: $$N_e P_e = 8000$$
4. The total number of items (books and exercise books) is 86: $$N_b + N_e = 86$$

Substitute $P_b = 3 P_e$ into the equation for the cost of books:

$$N_b (3 P_e) = 9600$$ $$3 N_b P_e = 9600$$ $$N_b P_e = \frac{9600}{3}$$ $$N_b P_e = 3200 \implies N_b = \frac{3200}{P_e}$$

From the equation for the cost of exercise books:

$$N_e P_e = 8000 \implies N_e = \frac{8000}{P_e}$$

Substitute the expressions for $N_b$ and $N_e$ into the total number of items equation ($N_b + N_e = 86$):

$$\frac{3200}{P_e} + \frac{8000}{P_e} = 86$$

Combine the terms on the left side:

$$\frac{3200 + 8000}{P_e} = 86$$ $$\frac{11200}{P_e} = 86$$

Now, solve for $P_e$:

$$P_e = \frac{11200}{86}$$

Simplify the fraction by dividing the numerator and denominator by 2:

$$P_e = \frac{5600}{43}$$

Using the relationship $P_b = 3 P_e$:

$$P_b = 3 \times \frac{5600}{43}$$ $$P_b = \frac{16800}{43}$$

a) Find the price of an exercise book.
The price of an exercise book is $P_e$.

$$P_e = \frac{5600}{43} \text{ Naira}$$

As a decimal, $P_e \approx 130.23$ Naira.
The price of an exercise book is $\boxed{\frac{5600}{43} \text{ Naira}}$.

b) What is the difference between the price?
The difference between the price of a book and an exercise book is $P_b - P_e$.

$$\text{Difference} = P_b - P_e$$ $$\text{Difference} = \frac{16800}{43} - \frac{5600}{43}$$ $$\text{Difference} = \frac{16800 - 5600}{43}$$ $$\text{Difference} = \frac{11200}{43} \text{ Naira}$$

As a decimal, the difference $\approx 260.47$ Naira.
The difference between the prices is $\boxed{\frac{11200}{43} \text{ Naira}}$.