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Question :

What was the buying exchange rate of currency C with respect to currency L on that day?

Started 2 weeks ago by Shashank in

Option D is the correct answer.

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, the buying exchange rate of currency C with respect to currency L is 1.9 on
that day. 

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