How many units of currency A did the outlet buy on that day?

It is given that the base exchange rates of A, B and C with respect to L are in the ratio 100:120:1. Let us assume that base exchange rates are '100a', '120a' and 'a' in that order.

It is given that the buying exchange rates of each of A, B, and C with respect to L are 5% below the corresponding base exchange rates. Therefore, we can say that the buying exchange rates are 95a, 114a, 0.95a.

It is given that the selling exchange rates of each of A, B, and C with respect to L are 10% above their corresponding base exchange rates. Therefore, we can say that the selling exchange rates are 110a, 132a, 1.1a.

We know about the opening and closing units in stock for each currency. Let us draw the table accordingly.  

Let 'p', 'q' and 'r' be the number of units of currency A, B and C bought by the outlet on that day. 

Then, we can say that the outlet sold 'p - 800', 'q' and 'r-3000' units of currency A, B and C respectively. 

It is given that the amount of L used by the outlet to buy C equals the amount of L it received by selling C.

$$\Rightarrow$$ 0.95a*r = 1.1a*(r - 3000)

$$\Rightarrow$$ 0.15r = 3300

$$\Rightarrow$$ r = 22000

It is also given that the amounts of L used by the outlet to buy A and B are in the ratio 5:3.

$$\Rightarrow$$ $$\dfrac{p*95a}{q*114a} = \dfrac{5}{3}$$

$$\Rightarrow$$ p = 2q

Also, the amounts of L the outlet received from the sales of A and B are in the ratio 5:9.

$$\Rightarrow$$ $$\dfrac{(p-800)*110a}{q*132a} = \dfrac{5}{9}$$

$$\Rightarrow$$ $$\dfrac{(2q-800)*110a}{q*132a} = \dfrac{5}{9}$$

$$\Rightarrow$$ q = 600

Therefore, p = 2q = 2*600 = 1200.

It is given that the outlet received 88000 units of L by selling A during the day.

$$\Rightarrow$$ (p-800)*110a = 88000

$$\Rightarrow$$ (1200-800)*110a = 88000

$$\Rightarrow$$ 44000a = 88000

$$\Rightarrow$$ a = 2

We can fill the entire table and answer all the questions. 

From the table we can see that the currency outlet bought 1200 units of A.