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CAT 2018 LRDI Questions 146

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 No. 1:
How many units of currency A did the outlet buy on that day?

Question No. 2:
How many units of currency C did the outlet sell on that day?
Options:
1. 19000
2. 3000
3. 6000
4. 22000

Question No. 3:
What was the base exchange rate of currency B with respect to currency L on that day?

Question No. 4:
What was the buying exchange rate of currency C with respect to currency L on that day?
Options:
1. 0.95
2. 1.10
3. 1.90
4. 2.20

The base exchange rates of currencies A, B and C with  respect to L is in the ratio 100 : 120 : 1.

The given information can be tabulated as follows

The outlet received 88,000 units of L by selling A and the ratio of amounts of L used to by A and B are in the ratio 5 : 3 and from the sales of A and B are in the ratio 5 : 9.

This set is best solved by looking at the choices for the question which asked for the base exchange rate of currency C. From that we have only two possible value for the base exchange rates for A, B and C 100,120 and 1 or 200, 240 and 2.

Assuming L to be100 for A.

Units sold of $\mathrm { A } = \frac { 88,000 } { 110 } = 800$

As the net addition is 800, the units of A bought is 1600 Amount of L used in buying 1600 units is 1600 x 0.95

x 100 = 152000 As the amount used to buy A and B are in the ratio 5 : 3, the amount used to buy B is $\frac { 152000 } { 5 } \times 3 = 91,200$

Number of units of B bought = $\frac { 91,200 } { 114 } = 800$

As the net addition of B is zero, number of units of B sold = 800.

The amount received = 800 x 132 = 105600

The amount received form selling A = 88,000

As 88,000 : 105600 is not in the ratio 5 : 9 as given in the data the base exchange rate for A is not 100 and has to be 200.

Units sold for $\mathrm { A } = \frac { 88000 } { 220 } = 400$

As net addition is 800, the units of A bought is 1200.

Amount of L used in buying 1200 units of A = 1200 x 0.95 x 2000 = 228000.

As the amount used to buy A and B are in the ratio 5 :3, quantity of L used to buy B is $\frac { 228000 } { 5 } \times 3 = 136800$

Number of units of $\mathrm { B }$ bought $= \frac { 136800 } { 228 } = 600$

As the net addition in B is zero, the number of units of B sold = 600.

The amount received from selling B = 600 x 264= 158400

The amount received from selling A = 88,000

The required ratio $\frac { 88,000 } { 158400 } = \frac { 5 } { 9 }$

Question 1:

Number of units of currency A bought 400 + 800 = 1200

Question 2:

As the net addition in the number of units of C is 3,000 and the buying and selling rates are in the ratio 0.95 and 1.1, assuming x units are sold 0.95 (x + 3000) = 1.1 (x)

0.15x = 2850

X= 19000

Question 3:

The base exchange rate of currency B with respect to L is 240.

Question 4:

The buying exchange rate of currency C with respect to L on that day was 1.90.

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