Comprehension
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.
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: 1
How many units of currency A did the outlet buy on that day?
How many units of currency A did the outlet buy on that day?
Updated On: Jul 29, 2025
Hide Solution
Verified By Collegedunia
Correct Answer: 1200
Solution and Explanation
Given:
- Exchange rates: A : B : C = 100 : 120 : 1
- 88000 units of L received by selling currency A
- Ratio of L used to buy A and B = 5 : 3
- Ratio of L received from selling A and B = 5 : 9
Assumption 1: Base exchange rate of A = 100
- Sell rate of A = 110 → Units sold = \( \frac{88000}{110} = 800 \)
- Net addition = 800 → Units bought = 1600
- L used to buy A = \(1600 \times 0.95 \times 100 = 152000\)
- L used to buy B = \( \frac{3}{5} \times 152000 = 91200 \)
- Buy rate of B = 114 → Units bought = \( \frac{91200}{114} = 800 \)
- B sold = 800 → L received = \( 800 \times 132 = 105600 \)
- L received from A = 88000
- Sales ratio = \( \frac{88000}{105600} \neq \frac{5}{9} \) ⇒ ❌ Not valid
Assumption 2: Base exchange rate of A = 200
- Sell rate of A = 220 → Units sold = \( \frac{88000}{220} = 400 \)
- Net addition = 800 → A bought = 1200 units
- L used to buy A = \( 1200 \times 0.95 \times 200 = 228000 \)
- L used to buy B = \( \frac{3}{5} \times 228000 = 136800 \)
- Buy rate of B = 228 → B bought = \( \frac{136800}{228} = 600 \)
- B sold = 600 → L received = \( 600 \times 264 = 158400 \)
- L received from A = 88000
- Sales ratio = \( \frac{88000}{158400} = \frac{5}{9} \) ⇒ ✅ Valid
Conclusion:
The correct base exchange rates are:
- A : B : C = 200 : 240 : 2
- Total units of A bought = 400 (sold) + 800 (net addition) = 1200
✔ Final Answer: Number of units of currency A bought = 1200
Was this answer helpful?
0
0
Question: 2
How many units of currency C did the outlet sell on that day?
How many units of currency C did the outlet sell on that day?
Updated On: Jul 29, 2025
- 19000
- 3000
- 6000
- 22000
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Given:
- Base exchange rates of currencies A, B, and C with respect to L are in the ratio: 100 : 120 : 1
- The outlet received 88,000 units of L by selling A
- L used to buy A and B are in the ratio 5 : 3
- L received from sales of A and B are in the ratio 5 : 9
Case 1: Assume Base Rate for A is 100
- Selling rate of A = 110 ⇒ Units of A sold = \( \frac{88000}{110} = 800 \)
- Net addition = 800 ⇒ Units of A bought = 1600
- L used to buy A = \(1600 \times 0.95 \times 100 = 152000\)
- L used to buy B = \( \frac{3}{5} \times 152000 = 91200 \)
- B buy rate = 114 ⇒ Units bought = \( \frac{91200}{114} = 800 \)
- B sold = 800 ⇒ L received = \(800 \times 132 = 105600\)
- L received from A = 88000
- Ratio of receipts = \( \frac{88000}{105600} \ne \frac{5}{9} \) ⇒ ❌ Doesn't match
Case 2: Assume Base Rate for A is 200
- Selling rate of A = 220 ⇒ Units of A sold = \( \frac{88000}{220} = 400 \)
- Net addition = 800 ⇒ Units of A bought = 1200
- L used to buy A = \(1200 \times 0.95 \times 200 = 228000\)
- L used to buy B = \( \frac{3}{5} \times 228000 = 136800 \)
- B buy rate = 228 ⇒ Units bought = \( \frac{136800}{228} = 600 \)
- B sold = 600 ⇒ L received = \(600 \times 264 = 158400\)
- L received from A = 88000
- Ratio = \( \frac{88000}{158400} = \frac{5}{9} \) ⇒ ✅ Matches
Conclusion for A and B:
- Base exchange rates are: A = 200, B = 240, C = 2
- Units of A bought = 400 + 800 = 1200
Now, Solve for Currency C
Net addition in units of C = 3000
Buy rate = 0.95, Sell rate = 1.1
Let \(x\) = units of C sold
We set up the equation using the money balance:
\[ 0.95(x + 3000) = 1.1x \]
\[ 0.95x + 2850 = 1.1x \Rightarrow 1.1x - 0.95x = 2850 \Rightarrow 0.15x = 2850 \Rightarrow x = \frac{2850}{0.15} = 19000 \]
✅ Final Answer:
- Units of currency C sold = 19000
Was this answer helpful?
0
0
Question: 3
What was the base exchange rate of currency B with respect to currency L on that day?
What was the base exchange rate of currency B with respect to currency L on that day?
Updated On: Jul 29, 2025
Hide Solution
Verified By Collegedunia
Correct Answer: 240
Solution and Explanation
Given:
- Base exchange rates of A : B : C with respect to L are in the ratio 100 : 120 : 1.
- Outlet received 88,000 units of L by selling currency A.
- L used to buy A and B is in the ratio 5 : 3.
- L received from selling A and B is in the ratio 5 : 9.
Case 1: Base Exchange Rate for A = 100
- Sell price of A = 110 ⇒ Units of A sold = \( \frac{88000}{110} = 800 \)
- Net addition in A = 800 ⇒ A bought = 1600 units
- L used to buy A = \( 1600 \times 0.95 \times 100 = 152000 \)
- L used to buy B = \( \frac{3}{5} \times 152000 = 91200 \)
- B buy rate = 114 ⇒ B bought = \( \frac{91200}{114} \approx 800 \)
- B sold = 800 units ⇒ L received = \( 800 \times 132 = 105600 \)
- L received from A = 88000
- Check sales ratio: \( \frac{88000}{105600} \neq \frac{5}{9} \) ⇒ ❌
Case 2: Base Exchange Rate for A = 200
- Sell price of A = 220 ⇒ A sold = \( \frac{88000}{220} = 400 \)
- Net addition = 800 ⇒ A bought = 1200 units
- L used to buy A = \( 1200 \times 0.95 \times 200 = 228000 \)
- L used to buy B = \( \frac{3}{5} \times 228000 = 136800 \)
- B buy rate = 228 ⇒ B bought = \( \frac{136800}{228} = 600 \)
- B sold = 600 units ⇒ L received = \( 600 \times 264 = 158400 \)
- A sales L received = 88000
- Check sales ratio: \( \frac{88000}{158400} = \frac{5}{9} \) ⇒ ✅
✔ Therefore, the correct base exchange rates are:
A : B : C = 200 : 240 : 2
Final Answer: The base exchange rate of currency B with respect to L is 240.
Was this answer helpful?
0
0
Question: 4
What was the buying exchange rate of currency C with respect to currency L on that day?
What was the buying exchange rate of currency C with respect to currency L on that day?
Updated On: Jul 29, 2025
- 0.95
- 1.10
- 1.90
- 2.20
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Base Exchange Ratio: A : B : C = 100 : 120 : 1 (initially assumed)
Given:
- Total units of L received from selling A = 88,000
- Ratio of L used to buy A and B = 5 : 3
- Ratio of amounts received from sales of A and B = 5 : 9
Case 1: Assume base exchange rates are 100, 120, and 1
- Sell price of A = 110 ⇒ Units of A sold = 88,000 / 110 = 800
- Net addition = 800 ⇒ Units of A bought = 1600
- L used to buy A = \(1600 \times 0.95 \times 100 = 152000\)
- L used to buy B = \(152000 \times \frac{3}{5} = 91200\)
- B buy rate = 114 ⇒ Units of B bought = 91200 / 114 = 800
- Since net addition in B is zero ⇒ Sold B = 800 units
- L received from B = \(800 \times 132 = 105600\)
- L received from A = 88000 ⇒ Total ratio = 88000 : 105600 ≠ 5 : 9 ❌
Case 2: Try base rates of 200, 240, and 2
- Sell price of A = 220 ⇒ Units of A sold = 88000 / 220 = 400
- Net addition = 800 ⇒ Units of A bought = 1200
- L used to buy A = \(1200 \times 0.95 \times 200 = 228000\)
- L used to buy B = \(228000 \times \frac{3}{5} = 136800\)
- B buy rate = 228 ⇒ Units bought = 136800 / 228 = 600
- Sold B = 600 units ⇒ L received = \(600 \times 264 = 158400\)
- L received from A = 88000 ⇒ Ratio = 88000 : 158400 = 5 : 9 ✔
Thus, the correct base rates are: A = 200, B = 240, C = 2
Required: Buying exchange rate of currency C with respect to L
⇒ Answer: 1.90
Was this answer helpful?
0
0
Top Questions on Conclusion
- Faculty members in a management school can belong to one of four departments – Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively. Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q. Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below.
1. There cannot be more than two candidates from a single department.
2. A candidate cannot vote for himself/herself.
3. Faculty members cannot vote for a candidate from their own department.
After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi - There are only four neighbourhoods in a city-Levmisto, Tyhrmisto,Pesmisto and Kitmisto. During the onset of a pandemic,the number of new cases of a disease in each of these neighbourhoods was recorded over a period of five days. On each day, the number of new cases recorded in any of the neighbourhoods was either 0,1,2 or 3.
The following facts are also known:
1. There was at least one new case in every neighbourhood on Day 1.
2. On each of the five days, there were more new cases in Kitmisto than in Pesmisto.
3. The number of new cases in the city in a day kept increasing during the five-day period. The number of new cases on Day 3 was exactly one more than that on Day 2.
4. The maximum number of new cases in a day in Pesmisto was 2 and this happenedonly once during the five-day period.
5. Kitmisto is the only place to have 3 new cases on Day 2.
6. The total numbers of new cases in Levmisto,Tyhrmisto,Pesmisto and Kitmisto over the five-day period were 12,12,5 and 14 respectively. - The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students - A, B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department.
Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00 am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots.
The following additional facts are also known.
1. Seminars by students from Economics are scheduled in each of the four slots.
2. A’s is the only seminar that is scheduled at 10:00 am. A is guided by R.
3. F is an Anthropology student whose seminar is scheduled at 10:30 am.
4. The seminar of a Sociology student is scheduled at 9:00 am.
5. B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student, who is guided by T, is also scheduled in the same slot.
6. P, who is guiding both B and C, has students scheduled in the first two slots.
7. A and G are scheduled in two consecutive slots. - Ten musicians (A, B, C, D, E, F, G, H, I and J) are experts in at least one of the following three percussion instruments: tabla, mridangam, and ghatam. Among them, three are experts in tabla but not in mridangam or ghatam, another three are experts in mridangam but not in tabla or ghatam, and one is an expert in ghatam but not in tabla or mridangam. Further, two are experts in tabla and mridangam but not in ghatam, and one is an expert in tabla and ghatam but not in mridangam.
The following facts are known about these ten musicians.
1. Both A and B are experts in mridangam, but only one of them is also an expert in tabla.
2. D is an expert in both tabla and ghatam.
3. Both F and G are experts in tabla, but only one of them is also an expert in mridangam.
4. Neither I nor J is an expert in tabla.
5. Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam. - A large store has only three departments, Clothing, Produce, and Electronics. The following figure shows the percentages of revenue and cost from the three departments for the years 2016, 2017 and 2018. The dotted lines depict percentage levels. So for example, in 2016, 50% of store's revenue came from its Electronics department while 40% of its costs were incurred in the Produce department.
In this setup, Profit is computed as (Revenue – Cost) and Percentage Profit as Profit/Cost × 100%.
It is known that
1. The percentage profit for the store in 2016 was 100%.
2. The store’s revenue doubled from 2016 to 2017, and its cost doubled from 2016 to 2018.
3. There was no profit from the Electronics department in 2017.
4. In 2018, the revenue from the Clothing department was the same as the cost incurred in the Produce department.
View More Questions
Questions Asked in CAT exam
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
- Logarithms
When $10^{100}$ is divided by 7, the remainder is ?
- CAT - 2024
- Basics of Numbers
- If $(a + b\sqrt{n})$ is the positive square root of $(29 - 12\sqrt{5})$, where $a$ and $b$ are integers, and $n$ is a natural number, then the maximum possible value of $(a + b + n)$ is ?
- CAT - 2024
- Algebra
- A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm, of the square ACEG is
- CAT - 2024
- Mensuration
- Let $x$, $y$, and $z$ be real numbers satisfying
\(4(x^2 + y^2 + z^2) = a,\)
\(4(x - y - z) = 3 + a.\)
Then $a$ equals ?- CAT - 2024
- Algebra
View More Questions