Question : The ratio of the sum of the salaries of A and B to the difference between their salaries is 11 : 1, and the ratio of the sum of the salaries of B and C to the difference between their salaries is also 11 : 1. If A's salary is the highest and C's is the lowest, then what is B's salary (in Rs.) given that the total of all their salaries is Rs. 1,82,000?
Option 1: Rs. 72,000
Option 2: Rs. 60,000
Option 3: Rs. 50,000
Option 4: Rs. 86,400
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Correct Answer: Rs. 60,000
Solution :
Given: The salaries of A, B, and C are:
$\frac{\text{A+B}}{\text{A–B}}=\frac{11}{1}$
And, $\frac{\text{B+C}}{\text{B–C}}=\frac{11}{1}$
Applying componendo and dividendo, we get:
$\frac{\text{A}}{\text{B}}=\frac{12}{10}=\frac{6}{5}$
And, $\frac{\text{B}}{\text{C}}=\frac{12}{10}=\frac{6}{5}$
$\therefore$ A : B : C = 36 : 30 : 25
Let $\text{A = 36x; B = 30x; C = 25x}$.
Given: A + B + C = 1,82,000
⇒ $\text{ 36x + 30x + 25x = 182000}$
⇒ $\text{ 91x = 182000}$
⇒ $\text{ x = 2000}$
$\therefore$ Salary of B = 30 × 2000 = Rs. 60,000
Hence, the correct answer is Rs. 60,000.
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