Divide ₹ 8,300 among A, B and C such that 4 times A’s share, 5 times B’s share and 7 times C’s share may all be equal.

Given,

Let, 4A = 5B = 7C = k

Then, A = $\dfrac{k}{4}$, B = $\dfrac{k}{5}$, C = $\dfrac{k}{7}$

Total amount divided among A, B and C = ₹ 8,300

So,

$\Rightarrow \dfrac{k}{4} + \dfrac{k}{5} + \dfrac{k}{7} = 8300 \\[1em] \Rightarrow k\Big(\dfrac{1}{4} + \dfrac{1}{5} + \dfrac{1}{7}\Big) = 8300 \\[1em] \Rightarrow k\Big(\dfrac{35 + 28 + 20}{140}\Big) = 8300 \\[1em] \Rightarrow k\Big(\dfrac{83}{140}\Big) = 8300 \\[1em] \Rightarrow k = \dfrac{8300 \times 140}{83} \\[1em] \Rightarrow k = 14000$

Therefore,

A' share = $\dfrac{14000}{4}$ = ₹ 3,500

B's share = $\dfrac{14000}{5}$ = ₹ 2,800

C"s share = $\dfrac{14000}{7}$ = ₹ 2,000

Hence, A = ₹ 3,500, B = ₹ 2,800 and C = ₹ 2,000.