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The base exchange rate of a currency X with respect to a currency Y is the number of units of currency Y which is equivalent in value to one unit of currency X. Currency exchange outlets buy currency at buying exchange rates that are lower than base exchange rates, and sell currency at selling exchange rates that are higher than base exchange rates.

A currency exchange outlet uses the local currency L to buy and sell three international currencies A, B, and C, but does not exchange one international currency directly with another. The base exchange rates of A, B and C with respect to L are in the ratio 100:120:1. The buying exchange rates of each of A, B, and C with respect to L are 5% below the corresponding base exchange rates, and their selling exchange rates are 10% above their corresponding base exchange rates.

The following facts are known about the outlet on a particular day:

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

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

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

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

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

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

Question 3 : What was the base exchange rate of currency B with respect to currency L on that day? [TITA]

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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.

Let us say the base rate of A w.r.t to L is 100k, then the base rate of B w.r.t to L is 120k and that of C is 1k.

To buy one unit of A, we need 95k units of L; if we sell one unit of A, we will get 110k units of L.

To buy one unit of B, we need 114k units of L; if we sell one unit of B, we will get 132k units of L.

To buy one unit of C, we need 0.95k units of L; if we sell one unit of C, we will get 1.1k units of L.

Let us keep this in mind and then build on this.

From statements 3 and 4,

Amounts of L received from sales of B = 88000 × \\frac{9}{5}) = 158400.

Number of units of A sold = \\frac{88000}{110K}) = \\frac{800}{K}).

Number of units of B sold = \\frac{158400}{132K}) = \\frac{1200}{K}).

The number of units of B is unchanged. What does this say?

Number of units of B bought = \\frac{1200}{K}).

Number of L used to buy this B = \\frac{1200}{K}) × 114K = 136800.

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

Or, the amount of L used to buy A = 136800 × \\frac{5}{3}) = 228000.

Number of units of A bought = \\frac{228000}{95K}) = \\frac{2400}{K}).

Number of units of A sold = \\frac{800}{K}). What is the value of K?

Number of units of A added = \\frac{1600}{K}). This is equal to 800 or, K = 2. The base exchange rates are 200, 240 and 2.

Or,

To buy one unit of A, we need 190 units of L; if we sell one unit of A, we will get 220 units of L.

To buy one unit of B, we need 228 units of L; if we sell one unit of B, we will get 264 units of L.

To buy one unit of C, we need 1.9 units of L; if we sell one unit of C, we will get 2.2k units of L.

Now, let us think about currency C.

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

We also know that we add 3000 units of C during the day.

If the number of units of L for transacting with C were to be called X. We would buy \\frac{L}{1.9}) units of C and sell \\frac{L}{2.2}) units of C.

We would add \\frac{L}{1.9}) - \\frac{L}{2.2}) units of C during the day.

Or, we know that \\frac{L}{1.9}) - \\frac{L}{2.2}) = 3000.

\\frac{2.2L − 1.9L}{1.9 × 2.2}) = 3000 or, L = 1000 × 1.9 × 2.2 = 41800.

Now, let us recap whatever we have thus far.

Currency A: We spend 228000 units of L to buy 1200 units of A, we receive 88000 units of L by selling 400 units of A. We add a total of 800 units of A.

Currency B: We spend 136800 units of L to buy 600 units of B, we receive 158400 units of L by selling 600 units of B. We add 0 units of B.

Currency C: We spend 41800 units of L to buy 22000 units of C, we receive 41800 units of L by selling 19000 units of C. We add 3000 units of C.

Let us move on to the questions.

From the inferences, the base exchange rate of currency B with respect to currency L on that day is 240

The question is **"What was the base exchange rate of currency B with respect to currency L on that day? [TITA]" **

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