The ratio of the sum of the salaries of A and B to the difference of their salaries is 11: 1. The ratio of the sum of the salaries of B and C to the difference of 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 ₹), given that the total of their salaries is ₹18,200?

The ratio of the sum of the salaries of A and B to the difference of their salaries is 11: 1.

Let's assume the salaries of A, B and C are 'a', 'b' and 'c' respectively.

$$\frac{a+b}{a-b}\ =\ \frac{11}{1}$$

a+b = 11a-11b

11a-a = 11b+b

10a = 12b

5a = 6b

a : b = 6 : 5    Eq.(i)

The ratio of the sum of the salaries of B and C to the difference of their salaries is also 11 : 1.

$$\frac{b+c}{b-c}\ =\ \frac{11}{1}$$

b+c = 11b-11c

11b-b = 11c+c

10b = 12c

5b = 6c

b : c = 6 : 5    Eq.(ii)

Merge Eq.(i) and Eq.(ii) by multiplying 6 and 5 respectively.

 a : b : c = $$6\times6 : 5\times6 : 5\times5$$

= 36 : 30 : 25

Let's assume a = 36y, b = 30y and c = 25y.

total of their salaries is ₹18,200.

36y+30y+25y = 18200

91y = 18200

y = 200

B's salary = b = 30y

= $$30\times200$$

= ₹6000