Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase and decrease was either by Rs. 1 crore or by Rs. 2 crores.
The table below provides partial information about the five firms.
| Firm | First year of existence | Last year of existence | Total amount raised (Rs. crores) |
|---|---|---|---|
| Alfloo | 2009 | 2016 | 21 |
| Bzygoo | 2012 | 2015 | |
| Czechy | 2013 | 9 | |
| Drjbna | 2011 | 2015 | 10 |
| Elavalaki | 2010 | 13 |
For which firm(s) can the amounts raised by them be concluded with certainty in each year?
- Only Bzygoo and Czechy and Drjbna
- Only Czechy
- Only Czechy and Drjbna
- Only Drjbna
The Correct Option is C
Solution and Explanation
The following data represents the possible cases for five companies:
| 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | |
| 1 | 2 | 3 | 4 | 5 | 3 | 2 | 1 | |
| 1 | 2 | 3 | 5 | 4 | 3 | 2 | 1 |
| 2012 | 2013 | 2014 | 2015 | |
| 1 | 2 | 3 | 1 | |
| 1 | 3 | 3 | 1 |
| 2013 | 2014 | 2015 | 2016 | 2017 | |
| 1 | 2 | 3 | 2 | 1 |
| 2011 | 2012 | 2013 | 2014 | 2015 | |
| 1 | 2 | 4 | 2 | 1 |
| 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | |
| 1 | 3 | 5 | 3 | 1 | - | |
| 1 | 2 | 3 | 4 | 2 | 1 | |
| 1 | 2 | 4 | 3 | 2 | 1 |
The amounts raised by Company C (Czechy) and Company D (Drjbna) can be definitively determined.
Correct option: (C) Only Czechy and Drjbna.
What best can be concluded about the total amount of money raised in 2015?
- It is either Rs. 7 crores or Rs. 8 crores or Rs. 9 crores.
- It is either Rs. 7 crores or Rs. 8 crores.
- It is either Rs. 8 crores or Rs. 9 crores.
- It is exactly Rs. 8 crores.
The Correct Option is B
Solution and Explanation
Total Funds Raised in 2015
Constraints:
- Each firm raises ₹1 crore in its initial and final years of operation.
- Annual fund amounts vary by ₹1 crore or ₹2 crores from the previous year.
- No firm raises the identical amount in consecutive years.
Firm Data:
| Firm | Years Active | Total Raised |
|---|---|---|
| Alfloo | 2009–2016 (8 years) | ₹21 crore |
| Bzygoo | 2012–2015 (4 years) | Unknown |
| Drjbna | 2011–2015 (5 years) | ₹10 crore |
Analysis:
- Drjbna: ₹1 crore raised in 2011 (first year) and ₹1 crore in 2015 (last year), totaling ₹2 crore.
- The remaining ₹8 crore must be distributed across 2012, 2013, and 2014. Possible sequences that adhere to the ₹1/₹2 crore change and no consecutive identical amounts exist. For example, a sequence of ₹2 crore, ₹4 crore, ₹2 crore yields ₹8 crore for these years. Therefore, Drjbna's amount in 2015 is ₹1 crore.
- Bzygoo: Operates for 4 years. ₹1 crore raised in the first year and ₹1 crore in the last year, totaling ₹2 crore. The remaining amount must be distributed across the two middle years (2013 and 2014). For instance, if the middle years raise ₹3 crore and ₹2 crore respectively, the total raised by Bzygoo would be ₹1 + ₹3 + ₹2 + ₹1 = ₹7 crore. If the middle years raise ₹2 crore and ₹3 crore respectively, the total raised by Bzygoo would be ₹1 + ₹2 + ₹3 + ₹1 = ₹7 crore. Other combinations are possible, leading to a total of ₹7 crore as one potential scenario.
Conclusion: Considering Drjbna raised ₹1 crore in 2015 and Bzygoo raised ₹6 crore total (with ₹1 crore in 2015), the combined total for 2015 could be ₹1 + ₹1 = ₹2 crore. Evaluating all valid combinations reveals other possibilities.
Final Answer:
The most probable total amount raised in 2015 is ₹7 crore.
What is the largest possible total amount of money (in Rs. crores) that could have been raised in 2013?
Solution and Explanation
The following presents possible scenarios for five companies:
| 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | |
|---|---|---|---|---|---|---|---|---|
| A | 1 | 2 | 3 | 4 | 5 | 3 | 2 | 1 |
| 1 | 2 | 3 | 5 | 4 | 3 | 2 | 1 |
| B | 2012 | 2013 | 2014 | 2015 |
|---|---|---|---|---|
| 1 | 2 | 3 | 1 | |
| 1 | 3 | 3 | 1 |
| C | 2013 | 2014 | 2015 | 2016 | 2017 |
|---|---|---|---|---|---|
| 1 | 2 | 3 | 2 | 1 |
| D | 2011 | 2012 | 2013 | 2014 | 2015 |
|---|---|---|---|---|---|
| 1 | 2 | 4 | 2 | 1 |
| E | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 |
|---|---|---|---|---|---|---|
| 1 | 3 | 5 | 3 | 1 | - | |
| 1 | 2 | 3 | 4 | 2 | 1 | |
| 1 | 2 | 4 | 3 | 2 | 1 |
The highest amount of money raised in 2013 was:
$5 + 3 + 1 + 4 + 4 = 17$
Therefore, the correct answer is 17 crores.
If Elavalaki raised Rs. 3 crores in 2013, then what is the smallest possible total amount of money (in Rs. crores) that could have been raised by all the companies in 2012?
- 12
- 9
- 11
- 10
The Correct Option is C
Solution and Explanation
To resolve this issue, we examine the given parameters and known figures. For each company:
- The initial and final fundraising amounts are ₹1 crore.
- Fundraising amounts increase and subsequently decrease by ₹1 crore or ₹2 crores annually.
- Fundraising amounts cannot be identical in two consecutive years.
Provided Information:
- Elavalaki raised ₹3 crores in 2013.
- Elavalaki commenced operations in 2010 and accumulated a total of ₹13 crores.
Hypothesized Annual Pattern for Elavalaki (aiming for a total of ₹13 crores):
| Year | Amount Raised (₹ crores) |
|---|---|
| 2010 | $1$ |
| 2011 | $3$ |
| 2012 | $5$ |
| 2013 | $3$ |
| 2014 | $1$ |
Summation = $1 + 3 + 5 + 3 + 1 = 13$ crores ✅
Therefore, Elavalaki's fundraising in 2012 was ₹5 crores.
Other Companies:
- Alfloo: Maximum cumulative total of ₹21 crores. Selecting the lowest possible value for 2012 results in an assumed ₹2 crores.
- Bzygoo: Lacking specific data, ₹2 crores is assumed as a reasonable minimum for 2012.
- Drjbna: Total of ₹10 crores; 2012 should be close to the minimum. ₹2 crores is assumed.
- Czechy: Started in 2013, hence ₹0 in 2012.
Aggregate Fundraising in 2012:
$5 + 2 + 2 + 2 = \mathbf{11}$ crores
Conclusion: ₹11 crores represents the lowest achievable total amount raised by all companies in 2012.
If the total amount of money raised in 2014 is Rs. 12 crores, then which of the following is not possible?
- Bzygoo raised more money than Elavalaki in 2014.
- Alfloo raised the same amount of money as Bzygoo in 2014.
- Alfloo raised the same amount of money as Drjbna in 2013.
- Bzygoo raised the same amount of money as Elavalaki in 2013.
The Correct Option is D
Solution and Explanation
To identify the impossible scenario, we use the following information and constraints:
- Each firm's first and last year of operation involved raising Rs. 1 crore.
- Annual fundraising amounts for any firm could not be consecutive. Annual changes were limited to Rs. 1 crore or Rs. 2 crores.
Examining each firm:
- Alfloo (2009-2016): Total raised: Rs. 21 crores. Fundraising sequence: Rs. 1 crore (2009), subsequent fluctuations, concluding with Rs. 1 crore in 2016.
- Bzygoo (2012-2015): Total unknown. Possible fundraising amounts:
| Year | Amount Raised |
|---|---|
| 2012 | 1 |
| 2013 | x (2 or 3) |
| 2014 | y (3, 4, or 5) |
| 2015 | 1 |
- Bzygoo's total: 1 + x + y + 1 = 2 + x + y, dependent on x and y.
- Czechy (2013-unknown): Total raised: Rs. 9 crores.
- Drjbna (2011-2015): Total raised: Rs. 10 crores. Possible sequences: 1-2-3-2-1 or 1-3-2-3-1.
- Elavalaki (2010-unknown): Total raised: Rs. 13 crores; similar progression logic applies.
Evaluating each possibility:
- Bzygoo raised more than Elavalaki in 2014: This is possible if Bzygoo's 2014 amount (y) exceeds Elavalaki's 2014 amount, given flexible yearly allocations.
- Alfloo's total equaled Bzygoo's 2014 amount: This is possible through matching increases or decreases in fundraising.
- Alfloo's total equaled Drjbna's 2013 amount: Considering Alfloo's cumulative total, a match is feasible.
- Bzygoo's amount equaled Elavalaki's 2013 amount: This scenario contradicts Elavalaki's known annual progression.
Conclusion:
Bzygoo raised the same amount of money as Elavalaki in 2013, which contradicts Bzygoo's potential yearly fundraising figures.
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