If ₹ 5,100 be divided among A, B, C in such a way that A gets $\dfrac{2}{3}$ of what B gets and B gets $\dfrac{1}{4}$ of what C gets, find their respective shares.

Given,

A = $\dfrac{2}{3}$ of B and B = $\dfrac{1}{4}$ of C

Express all in terms of B:

A = $\dfrac{2}{3}B$, B = B and C = 4B

Total amount divided among A, B and C = ₹ 5,100

So,

$\Rightarrow \dfrac{2}{3}B + B + 4B = 5100 \\[1em] \Rightarrow \dfrac{2B + 3B + 12B}{3} = 5100 \\[1em] \Rightarrow \dfrac{17B}{3} = 5100 \\[1em] \Rightarrow B = \dfrac{5100 \times 3}{17} \\[1em] \Rightarrow B = ₹ 900.$

B's share = ₹ 900

Therefore,

A's share = $\dfrac{2}{3} \times 900$ = ₹ 600

C's share = 4 × 900 = ₹ 3,600

Hence, A = ₹ 600, B = ₹ 900 and C = ₹ 3,600.