Question

The monthly salary of Amar is two and a half times the monthly salary of Bakshi. The ratio of the monthly salaries of Bakshi and Chitra is the duplicate ratio of monthly salaries of Amar and Bakshi. The monthly salary of Chitra is thrice the monthly salary of Daksha. The ratio of monthly salaries of Daksha and Eeshwar is the triplicate of the ratio of monthly salaries of Chitra and Daksha. What is the monthly salary of Amar, if Eeshwar's monthly salary is Rs. 1,560?

• A. Rs. 19,74,375
• B. Rs. 12,75,375
• C. Rs. 9,37,675
• D. Rs. 7,89,750

Hint:

Convert each ratio statement into a chain of ratios and combine them using a common multiple.

Answer 1

The Correct Option is A

Step 1: Write the Amar-Bakshi ratio. Amar = 2.5 times Bakshi, so Amar : Bakshi = 2.5 : 1 = 5 : 2.
Step 2: Find the Bakshi-Chitra ratio. This is the duplicate (squared) ratio of Amar : Bakshi, so Bakshi : Chitra = \(5^2 : 2^2 = 25 : 4\).
Step 3: Express Chitra in terms of Bakshi (=B). From Bakshi : Chitra = 25 : 4, Chitra = \(\dfrac{4}{25}B\).
Step 4: Find Daksha. Chitra = thrice Daksha, so Daksha = Chitra/3 = \(\dfrac{4}{75}B\).
Step 5: Find the Daksha-Eeshwar ratio. Chitra : Daksha = 3 : 1 (since Chitra = 3 x Daksha). The triplicate (cubed) ratio is \(3^3 : 1^3 = 27 : 1\), so Daksha : Eeshwar = 27 : 1, meaning Eeshwar = Daksha/27.
Step 6: Express Eeshwar in terms of B. Eeshwar = \(\dfrac{4B/75}{27} = \dfrac{4B}{2025}\).
Step 7: Use the given value of Eeshwar's salary. \(\dfrac{4B}{2025} = 1560\), so \(B = \dfrac{1560 \times 2025}{4} = 789750\).
Step 8: Find Amar's salary. Amar = 2.5B = \(2.5 \times 789750 = 1974375\).\[\boxed{\text{Rs. }19{,}74{,}375}\]