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 ratio of the ratios 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
• E. Rs. 7,65,275

Hint:

Chain all five salaries back to one variable using the given ratios (remembering that a duplicate ratio squares the ratio and a triplicate ratio cubes it), then substitute Eeshwar's known salary to solve for that variable.

Answer 1

The Correct Option is A

Step 1: Relate Amar and Bakshi.
Let Bakshi's salary be \(B\). Amar's salary is \(2.5\) times Bakshi's:
$$A=\frac{5}{2}B$$
So \(A:B=5:2\).

Step 2: Relate Bakshi and Chitra using the duplicate ratio.
The duplicate ratio of \(A:B=5:2\) is \(25:4\), and this equals \(B:C\):
$$B:C=25:4 \implies C=\frac{4}{25}B$$

Step 3: Relate Chitra and Daksha.
Chitra's salary is thrice Daksha's, so \(C=3D\), which gives:
$$D=\frac{C}{3}=\frac{4}{75}B$$
Also, this means \(C:D=3:1\).

Step 4: Relate Daksha and Eeshwar using the triplicate ratio.
The triplicate ratio of \(C:D=3:1\) is \(27:1\), and this equals \(D:E\):
$$D:E=27:1 \implies E=\frac{D}{27}=\frac{4}{75\times27}B=\frac{4}{2025}B$$

Step 5: Use the given value of Eeshwar's salary.
Given \(E=1560\):
$$\frac{4}{2025}B=1560$$
$$B=1560\times\frac{2025}{4}=390\times2025=7,89,750$$

Step 6: Find Amar's salary.
$$A=\frac{5}{2}B=\frac{5}{2}\times7,89,750=2.5\times7,89,750=19,74,375$$
So Amar's monthly salary is Rs. 19,74,375. The correct option is (a) Rs. 19,74,375.