Divide ₹1,290 into A, B and C such that A is $\dfrac{2}{5}$ of B and B : C = 4 : 3.

Given, B : C = 4 : 3

If B = 4a, then C = 3a

Given, A is $\dfrac{2}{5}$ of B.

∴ A = $\dfrac{2}{5} \times 4a = \dfrac{8a}{5}$

Share of A,

$= \dfrac{A}{A + B + C} \times 1290 \\[1em] = \dfrac{\dfrac{8a}{5}}{\dfrac{8a}{5} + 4a + 3a} \times 1290 \\[1em] = \dfrac{\dfrac{8a}{5}}{\dfrac{8a + 20a + 15a}{5}} \times 1290 \\[1em] = \dfrac{8a}{43a} \times 1290 \\[1em] = \dfrac{8}{43} \times 1290 \\[1em] = 240.$

Share of B,

$= \dfrac{B}{A + B + C} \times 1290 \\[1em] = \dfrac{4a}{\dfrac{8a}{5} + 4a + 3a} \times 1290 \\[1em] = \dfrac{4a}{\dfrac{8a + 20a + 15a}{5}} \times 1290 \\[1em] = \dfrac{20a}{43a} \times 1290 \\[1em] = \dfrac{20}{43} \times 1290 \\[1em] = 600.$

Share of C,

$= \dfrac{C}{A + B + C} \times 1290 \\[1em] = \dfrac{3a}{\dfrac{8a}{5} + 4a + 3a} \times 1290 \\[1em] = \dfrac{3a}{\dfrac{8a + 20a + 15a}{5}} \times 1290 \\[1em] = \dfrac{15a}{43a} \times 1290 \\[1em] = \dfrac{15}{43} \times 1290 \\[1em] = 450.$

Hence, the amount of money with A = ₹ 240, B = ₹ 600 and C = ₹ 450.