Question

If ₹5100 be divided among A, B, C in such a way that A gets $$\frac{2}{3}$$ of what B gets and B gets $$\frac{1}{4}$$ of what C gets, find their respective shares.

Answer 1

Let C's share be ₹ $$x$$.

Then, B's share = $$\frac{1}{4}x$$.

A's share = $$\frac{2}{3} \times \left(\frac{1}{4}x\right) = \frac{1}{6}x$$. 

Total sum = $$A + B + C = 5100$$: $$\frac{1}{6}x + \frac{1}{4}x + x = 5100$$ 

Find common denominator (12):

$$\frac{2x + 3x + 12x}{12} = 5100$$

$$\implies \frac{17x}{12} = 5100$$ 

Solve for $$x$$: $$x = \frac{5100 \times 12}{17} = 300 \times 12 = 3600$$ 

Respective shares:

C's share = ₹ 3600

B's share = $$\frac{3600}{4} = \text{₹ } 900$$

A's share = $$\frac{3600}{6} = \text{₹ } 600$$