The ratio of the income of A and B as well as B and C is 3 : 2. If one - third of A's income exceeds one - fourth of C's income by Rs. 1000, what is B's income in Rs = ?

Given,
A : B = 3 : 2
B : C = 3 : 2
Equal the value of B in both equation
A : B = 3 : 2 (multiply with 3) and
B : C = 3 : 2 (multiply with 2)
i.e. A : B = 9 : 6 and
B : C = 6 : 4
∴ A : B : C = 9 : 6 : 4

Now $$\frac{A}{3}$$ - 1000 = $$\frac{C}{4}$$
i.e. $$\frac{9x}{3}$$ - 1000 = $$\frac{4x}{4}$$
⇒ 3x - 1000 = x
⇒ x = 500

∴ Income of B is = 6x = 6 × 500 = 3000