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 possible cases for all 5 companies are:
| 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 |
For Company C (Czechy) and Company D (Drjbna), we can definitively conclude the amounts raised.
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
Determining the Total Amount Raised in 2015
Given Constraints:
- Each firm raises ₹1 crore in its first and last years.
- Each year, the amount raised changes by ₹1 crore or ₹2 crores.
- No firm raises the same amount in two consecutive years.
Firms 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 |
Step-by-step Analysis:
- Drjbna: First and last years (2011 and 2015) contributed ₹1 crore each. That’s ₹2 crore.
- The remaining ₹8 crore must come from 2012, 2013, and 2014. We look for valid sequences with increasing/decreasing by ₹1 or ₹2 crore, no same consecutive values.
- One such valid sequence: ₹2 crore → ₹3 crore → ₹3 crore (not valid, has same consecutive). Another: ₹2 → ₹4 → ₹2 → Total = ₹8 crore. So Drjbna’s amount in 2015 = ₹1 crore.
- Bzygoo: Similar logic with 4 years. First and last years: ₹1 crore + ₹1 crore = ₹2 crore. Try valid distributions over 2 middle years (2013 and 2014) to total different sums (e.g. 2+3 or 3+2 gives 5). So total = 7 crore possible.
Conclusion: If Drjbna raised ₹1 crore in 2015 and Bzygoo raised ₹6 crore total (with ₹1 crore in 2015), then total in 2015 = ₹1 + ₹1 = ₹2 crore. Try all combinations respecting constraints.
Final Answer:
The total amount raised in 2015 is most plausibly ₹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 possible cases for all 5 companies are:
| 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 |
Maximum money raised in 2013:
$5 + 3 + 1 + 4 + 4 = 17$
So, 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 solve this problem, we analyze the constraints and known values. Each company:
- Starts and ends with ₹1 crore.
- Increases and then decreases fundraising amounts by ₹1 crore or ₹2 crores annually.
- No two consecutive years have the same amount.
Given:
- Elavalaki raised ₹3 crores in 2013.
- Elavalaki started in 2010 and raised ₹13 crores in total.
Assume the yearly pattern for Elavalaki (trying to fit total ₹13 crores):
| Year | Amount Raised (₹ crores) |
|---|---|
| 2010 | $1$ |
| 2011 | $3$ |
| 2012 | $5$ |
| 2013 | $3$ |
| 2014 | $1$ |
Total = $1 + 3 + 5 + 3 + 1 = 13$ crores ✅
So, Elavalaki in 2012 raised ₹5 crores.
Other companies:
- Alfloo: Max total ₹21 crores. Choose minimal value in 2012 → assume ₹2 crores.
- Bzygoo: No details, assume ₹2 crores as logical minimum for 2012.
- Drjbna: Total ₹10 crores; 2012 should be near minimum. Assume ₹2 crores.
- Czechy: Started in 2013 → ₹0 in 2012.
Total raised in 2012:
$5 + 2 + 2 + 2 = \mathbf{11}$ crores
Answer: ₹11 crores is the smallest possible 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 determine which option is not possible, let's proceed with the information and constraints provided. We know:
- Each firm raised Rs. 1 crore in its first and last year of existence.
- No firm raised the same amount in consecutive years, and annual changes were either Rs. 1 crore or Rs. 2 crores.
Now, consider each firm:
- Alfloo (2009-2016): Total Rs. 21 crores. It raises: Rs. 1 crore (2009), increases/decreases to a peak and returns to Rs. 1 crore in 2016.
- Bzygoo (2012-2015): Unknown total, its possibilities:
| Year | Amount Raised |
|---|---|
| 2012 | 1 |
| 2013 | x (2 or 3) |
| 2014 | y (3, 4, or 5) |
| 2015 | 1 |
- Depending on x and y, sum(Bzygoo) = 1 + x + y + 1 = (2 + x + y).
- Czechy (2013-unknown): Total Rs. 9 crores.
- Drjbna (2011-2015): Total Rs. 10 crores: Possibly 1-2-3-2-1 or 1-3-2-3-1.
- Elavalaki (2010-unknown): Total Rs. 13 crores; similar progression logic applies.
We explore each option:
- Bzygoo raised more than Elavalaki (2014): Possible if y > Elavalaki (2014), as allocations are flexible each year.
- Alfloo = Bzygoo (2014): Possible alignment of any increase/decrease to match funds raised.
- Alfloo = Drjbna (2013): Noting Alfloo's running total, a match is possible.
- Bzygoo = Elavalaki (2013): To have the same amount as Elavalaki in 2013 wouldn't align with their annual increase.
Therefore,
Bzygoo raised the same amount of money as Elavalaki in 2013, which doesn't fit Bzygoo's possible annual amounts.
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