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Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
- a)16 years
- b)18 years
- c)20 years
- d)Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
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Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Fou...
To solve this problem, let's assume the present ages of Kunal and Sagar to be '6x' years and '5x' years respectively.
Ratio of their ages 6 years ago:
Kunal's age 6 years ago = 6x - 6
Sagar's age 6 years ago = 5x - 6
Given that the ratio of their ages 6 years ago was 6 : 5, we can write the equation:
(6x - 6) / (5x - 6) = 6/5
Cross-multiplying, we get:
5(6x - 6) = 6(5x - 6)
30x - 30 = 30x - 36
30 = 36
This equation has no solution, which means that our assumption that their present ages are '6x' and '5x' is incorrect.
Let's assume their present ages as 'a' and 'b' years respectively.
Therefore, their ages 6 years ago would be 'a-6' and 'b-6' years respectively.
The given ratio of their ages 6 years ago is 6:5, which can be written as:
(a-6) / (b-6) = 6/5
Cross-multiplying, we get:
5(a-6) = 6(b-6)
5a - 30 = 6b - 36
5a - 6b = -36 + 30
5a - 6b = -6
Now, let's consider their ages 4 years from now as 'p' and 'q' years respectively.
The ratio of their ages 4 years from now is given as 11:10, which can be written as:
(p+4) / (q+4) = 11/10
Cross-multiplying, we get:
10(p+4) = 11(q+4)
10p + 40 = 11q + 44
10p - 11q = 44 - 40
10p - 11q = 4
Now, we have a system of two equations with two variables:
5a - 6b = -6 --(1)
10p - 11q = 4 --(2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve it using the method of elimination:
Multiplying equation (1) by 2, we get:
10a - 12b = -12 --(3)
Now, let's subtract equation (3) from equation (2):
10p - 11q - (10a - 12b) = 4 - (-12)
10p - 11q - 10a + 12b = 16
-10a + 10p + 12b - 11q = 16
Rearranging the equation, we get:
10p - 10a + 12b - 11q = 16
10(p - a) + 12(b - q) = 16
Dividing both sides by 2, we get:
5(p - a) + 6(b - q) = 8
This equation tells us that the left-hand side is an even number. However, the
Ratio of their ages 6 years ago:
Kunal's age 6 years ago = 6x - 6
Sagar's age 6 years ago = 5x - 6
Given that the ratio of their ages 6 years ago was 6 : 5, we can write the equation:
(6x - 6) / (5x - 6) = 6/5
Cross-multiplying, we get:
5(6x - 6) = 6(5x - 6)
30x - 30 = 30x - 36
30 = 36
This equation has no solution, which means that our assumption that their present ages are '6x' and '5x' is incorrect.
Let's assume their present ages as 'a' and 'b' years respectively.
Therefore, their ages 6 years ago would be 'a-6' and 'b-6' years respectively.
The given ratio of their ages 6 years ago is 6:5, which can be written as:
(a-6) / (b-6) = 6/5
Cross-multiplying, we get:
5(a-6) = 6(b-6)
5a - 30 = 6b - 36
5a - 6b = -36 + 30
5a - 6b = -6
Now, let's consider their ages 4 years from now as 'p' and 'q' years respectively.
The ratio of their ages 4 years from now is given as 11:10, which can be written as:
(p+4) / (q+4) = 11/10
Cross-multiplying, we get:
10(p+4) = 11(q+4)
10p + 40 = 11q + 44
10p - 11q = 44 - 40
10p - 11q = 4
Now, we have a system of two equations with two variables:
5a - 6b = -6 --(1)
10p - 11q = 4 --(2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve it using the method of elimination:
Multiplying equation (1) by 2, we get:
10a - 12b = -12 --(3)
Now, let's subtract equation (3) from equation (2):
10p - 11q - (10a - 12b) = 4 - (-12)
10p - 11q - 10a + 12b = 16
-10a + 10p + 12b - 11q = 16
Rearranging the equation, we get:
10p - 10a + 12b - 11q = 16
10(p - a) + 12(b - q) = 16
Dividing both sides by 2, we get:
5(p - a) + 6(b - q) = 8
This equation tells us that the left-hand side is an even number. However, the
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Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagars age at present?a)16 yearsb)18 yearsc)20 yearsd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?
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Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagars age at present?a)16 yearsb)18 yearsc)20 yearsd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagars age at present?a)16 yearsb)18 yearsc)20 yearsd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagars age at present?a)16 yearsb)18 yearsc)20 yearsd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagars age at present?a)16 yearsb)18 yearsc)20 yearsd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagars age at present?a)16 yearsb)18 yearsc)20 yearsd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagars age at present?a)16 yearsb)18 yearsc)20 yearsd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
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Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagars age at present?a)16 yearsb)18 yearsc)20 yearsd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagars age at present?a)16 yearsb)18 yearsc)20 yearsd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagars age at present?a)16 yearsb)18 yearsc)20 yearsd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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