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Two persons are awarded pensions in proportion to the square root of the number of years they have served. The second person's service period is 9 years longer than that of the first. If the length of service of the first person had exceeded that of the second by 4.25 years, their pensions would have been in the respective ratio of 9 : 8. How long have the two served?
- a)34 years, 43 years
- b)16 years, 7 years
- c)4 years, 13 years
- d)25 years, 34 years
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two persons are awarded pensions in proportion to the square root of t...
Let n be the number of years served by the second.
= 
= 64n + 272 = 81n
n = 16 years
First person's service = 16 - 9 = 7 years
Most Upvoted Answer
Two persons are awarded pensions in proportion to the square root of t...
Given Data:
- The pension is awarded in proportion to the square root of the number of years served.
- The second person's service period is 9 years longer than that of the first.
- If the length of service of the first person had exceeded that of the second by 4.25 years, their pensions would have been in the respective ratio of 9:8.
Let's Assume:
- The first person has served for x years.
- The second person has served for x + 9 years.
Calculating the Pensions:
- The pension for the first person is proportional to the square root of x: √x.
- The pension for the second person is proportional to the square root of (x + 9): √(x + 9).
Given Condition:
- If the length of service of the first person had exceeded that of the second by 4.25 years, their pensions would have been in the respective ratio of 9:8.
- This means that (√(x + 4.25))/(√x) = 9/8.
Solving the Equation:
- Cross multiplying, we get (8√(x + 4.25)) = (9√x).
- Squaring both sides, we get 64(x + 4.25) = 81x.
- Expanding and simplifying the equation, we get 64x + 272 = 81x.
- Rearranging the terms, we get 17x = 272.
- Dividing both sides by 17, we get x = 16.
Calculating the Length of Service:
- The first person has served for 16 years.
- The second person has served for 16 + 9 = 25 years.
Hence, the length of service for the first person is 16 years, and the length of service for the second person is 25 years (Option B).
- The pension is awarded in proportion to the square root of the number of years served.
- The second person's service period is 9 years longer than that of the first.
- If the length of service of the first person had exceeded that of the second by 4.25 years, their pensions would have been in the respective ratio of 9:8.
Let's Assume:
- The first person has served for x years.
- The second person has served for x + 9 years.
Calculating the Pensions:
- The pension for the first person is proportional to the square root of x: √x.
- The pension for the second person is proportional to the square root of (x + 9): √(x + 9).
Given Condition:
- If the length of service of the first person had exceeded that of the second by 4.25 years, their pensions would have been in the respective ratio of 9:8.
- This means that (√(x + 4.25))/(√x) = 9/8.
Solving the Equation:
- Cross multiplying, we get (8√(x + 4.25)) = (9√x).
- Squaring both sides, we get 64(x + 4.25) = 81x.
- Expanding and simplifying the equation, we get 64x + 272 = 81x.
- Rearranging the terms, we get 17x = 272.
- Dividing both sides by 17, we get x = 16.
Calculating the Length of Service:
- The first person has served for 16 years.
- The second person has served for 16 + 9 = 25 years.
Hence, the length of service for the first person is 16 years, and the length of service for the second person is 25 years (Option B).
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Two persons are awarded pensions in proportion to the square root of the number of years they have served. The second persons service period is 9 years longer than that of the first. If the length of service of the first person had exceeded that of the second by 4.25 years, their pensions would have been in the respective ratio of 9 : 8. How long have the two served?a)34 years, 43 yearsb)16 years, 7 yearsc)4 years, 13 yearsd)25 years, 34 yearsCorrect answer is option 'B'. Can you explain this answer?
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Two persons are awarded pensions in proportion to the square root of the number of years they have served. The second persons service period is 9 years longer than that of the first. If the length of service of the first person had exceeded that of the second by 4.25 years, their pensions would have been in the respective ratio of 9 : 8. How long have the two served?a)34 years, 43 yearsb)16 years, 7 yearsc)4 years, 13 yearsd)25 years, 34 yearsCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two persons are awarded pensions in proportion to the square root of the number of years they have served. The second persons service period is 9 years longer than that of the first. If the length of service of the first person had exceeded that of the second by 4.25 years, their pensions would have been in the respective ratio of 9 : 8. How long have the two served?a)34 years, 43 yearsb)16 years, 7 yearsc)4 years, 13 yearsd)25 years, 34 yearsCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two persons are awarded pensions in proportion to the square root of the number of years they have served. The second persons service period is 9 years longer than that of the first. If the length of service of the first person had exceeded that of the second by 4.25 years, their pensions would have been in the respective ratio of 9 : 8. How long have the two served?a)34 years, 43 yearsb)16 years, 7 yearsc)4 years, 13 yearsd)25 years, 34 yearsCorrect answer is option 'B'. Can you explain this answer?.
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