Multiple choice

In a tech startup in Bangalore, Ayan, Bhavya, Chetna, and Dhruv are close friends and colleagues with varying monthly salaries. Their monthly salary dynamics create an intriguing scenario: Ayan and Bhavya together earn in a month the equivalent of what Chetna earns in 9 months. Conversely, Chetna and Ayan together earn in a month what Bhavya earns in just 3 months. Dhruv, the fourth friend, earns in a month that is twice the amount Ayan earns monthly. Determine the ratio between the highest and lowest monthly salaries among Ayan, Bhavya, Chetna, and Dhruv.

  1. 13 : 1

  2. 17 : 4

  3. 13 : 3

  4. 12 : 5
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A Correct answer
Explanation

Let A, B, C, D be the salaries. Equations: A+B = 9C; C+A = 3B; D = 2A. From C+A=3B, C=3B-A. Substitute into A+B=9(3B-A) -> A+B = 27B-9A -> 10A = 26B -> A = 2.6B. Then C = 3B - 2.6B = 0.4B. D = 2A = 5.2B. Salaries are A=2.6B, B=B, C=0.4B, D=5.2B. Ratio of highest (D=5.2B) to lowest (C=0.4B) is 5.2/0.4 = 13/1.

AI explanation

Let the monthly salaries of Ayan, Bhavya, and Chetna be A, B, and C, respectively. The first statement gives A plus B equals 9C, and the second gives C plus A equals 3B, which simplifies to A equals 3B minus C. Substituting this into the first equation gives 3B minus C plus B equals 9C, meaning 4B equals 10C, so B equals 2.5C. Substituting this back gives A equals 3 times 2.5C minus C, which is 6.5C, and Dhruv earns twice Ayan's salary, making Dhruv's salary 13C. The highest salary is 13C and the lowest is C, making the required ratio 13 to 1.

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