What was the base exchange rate of currency B with respect to currency L on that day?

Currency	Buying rate	Base rate	Selling rate
A
B
C

We know, 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.

Currency	Buying rate	Base rate	Selling rate
A	95a	100a	110a
B	114a	120a	132a
C	0.95a	a	1.1a

Now, we are 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.

Similarly, their selling exchange rates are 10% above their corresponding base exchange rates.

=> we can say that the selling exchange rates are 110a, 132a, 1.1a.

In currency transactions, getting the basic outline is very important.

So, if the base rate of A w.r.t to L is 100, then to buy one unit of A, we need 95 units of L and if we sell one unit of A, we will get 110 units of L.

Currency	Buying rate	Base rate	Selling rate	Opening stock	Buy	Sell	Closing stock
A	95a	100a	110a	2500
B	114a	120a	132a	4800
C	0.95a	a	1.1a	48000

Using clue 5,

The outlet started the day with some amount of L, 2500 units of A, 4800 units of B, and 48000 units of C.

This clue gives us the opening stock of all the currencies with the exchange shop.

Currency	Buying rate	Base rate	Selling rate	Opening stock	Buy	Sell	Closing stock
A	95a	100a	110a	2500			3300
B	114a	120a	132a	4800			4800
C	0.95a	a	1.1a	48000			51000

Using clue 6 ;

The outlet ended the day with some amount of L, 3300 units of A, 4800 units of B, and 51000 units of C.

This clue gives us the closing stock of all the currencies with the exchange shop.

Currency	Buying rate	Base rate	Selling rate	Opening stock	Buy	Sell	Closing stock
A	95a	100a	110a	2500	p	p - 800	3300
B	114a	120a	132a	4800	q	q	4800
C	0.95a	a	1.1a	48000	r	r - 3000	51000

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

=> Number of units sold of A = p - $(3000 - 2500) =$ p - $800$

and, number of units sold of B = $q - (4800 - 4800) = q$

and, number of units sold of C = $r - (51000 - 48000) = r - 3000$

Currency	Buying rate	Base rate	Selling rate	Opening stock	Buy	Sell	Closing stock
A	95a	100a	110a	2500	p	p - 800	3300
B	114a	120a	132a	4800	q	q	4800
C	0.95a	a	1.1a	48000	22000	19000	51000

Clue 1 says,

The amount of L used by the outlet to buy C equals the amount of L it received by selling C.

⇒$0.95a*r = 1.1a*(r - 3000)$

⇒ $0.15r = 3300$

⇒ $r = 22000$

Currency	Buying rate	Base rate	Selling rate	Opening stock	Buy	Sell	Closing stock
A	95a	100a	110a	2500	p	p - 800	3300
B	114a	120a	132a	4800	600	600	4800
C	0.95a	a	1.1a	48000	22000	19000	51000

Clue 3 says,

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

=> $\frac{(p - 800) \cdot 110a}{q \cdot 132a} = \frac{5}{9}$

=>$\frac{(2q - 800) \cdot 110a}{q \cdot 132a} = \frac{5}{9}$

=> $q = 600$

Currency	Buying rate	Base rate	Selling rate	Opening stock	Buy	Sell	Closing stock
A	95a	100a	110a	2500	1200	400	3300
B	114a	120a	132a	4800	600	600	4800
C	0.95a	a	1.1a	48000	22000	19000	51000

Clue 2 says,

The amounts of L used by the outlet to buy A and B are in the ratio 5:3.

=> $\frac{p \cdot 95a}{q \cdot 114a} = \frac{5}{3}$

=> $p = 2q$

=> $p = 2 * 600$

=> $p = 1200$

Currency	Buying rate	Base rate	Selling rate	Opening stock	Buy	Sell	Closing stock
A	190	200	220	2500	1200	400	3300
B	228	240	264	4800	600	600	4800
C	1.9	2	2.2	48000	22000	19000	51000

Clue 4 says,

The outlet received 88000 units of L by selling A during the day.

⇒ $(p-800)*110a = 88000$

⇒ $(1200-800)*110a = 88000$

⇒ $44000a = 88000$

⇒ $a = 2$

Currency	Buying rate	Base rate	Selling rate	Opening stock	Buy	Sell	Closing stock
A	190	200	220	2500	1200	400	3300
B	228	240	264	4800	600	600	4800
C	1.9	2	2.2	48000	22000	19000	51000

the base exchange rate of currency B with respect to currency L was 240.