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Question :

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

Started 2 weeks ago by Shashank in

Answer : 1200

Explanatory Answer

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 × 9595 = 158400. 
Number of units of A sold = 88000110K88000110๐พ = 800K800๐พ. 
Number of units of B sold = 158400132K158400132๐พ = 1200K1200๐พ. 
The number of units of B is unchanged. What does this say? 
Number of units of B bought = 1200K1200๐พ. 
Number of L used to buy this B = 1200K1200๐พ × 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 × 5353 = 228000. 
Number of units of A bought = 22800095K22800095๐พ = 2400K2400๐พ. 
Number of units of A sold = 800K800๐พ. What is the value of K? 
Number of units of A added = 1600K1600๐พ. 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 L1.9๐ฟ1.9 units of C and sell L2.2๐ฟ2.2 units of C. 
We would add L1.9๐ฟ1.9 - L2.2๐ฟ2.2 units of C during the day. 
Or, we know that L1.9๐ฟ1.9 - L2.2๐ฟ2.2 = 3000. 
2.2L−1.9L1.9×2.22.2๐ฟ−1.9๐ฟ1.9×2.2 = 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, we can say that the outlet buys 1200 units of currency A on that day.

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