A, B and started a business with their capitals in the ratio 4 : 2 : 9. At the end of every quarter, A halves his capital, whereas B doubles his capital and C leaves his capital unchanged. If at the end of a year, A’s profit was ₹24,000, then what is the total profit (in ₹) is

A, B, and C started the business with their capital in ratio = 4: 2: 9 

lets A's initial capital = $$4x$$

B's initial capital = $$ 2x $$

C's initial capital = $$ 9x $$ 

Haves his capital quarterly, B doubles his capital quarterly and C keeps his capital unchanged.

so total capital of A = $$ 4x \times 3 + 2x \times 3 + x \times 3 + \dfrac {x}{2}\times 3 $$

$$ \Rightarrow (4x + 2x + x + \dfrac {x}{2})\times 3 $$

$$\Rightarrow \dfrac {15x}{2} \times 3 $$

total capital of B = $$ 2x \times 3 + 4x \times 3 + 8x \times 3 + 16x \times 3 $$ 

$$\Rightarrow (2x + 4x+8x+16x) \times 3 $$

$$\Rightarrow 30 x \times 3 $$ 

total capital of C = $$9x \times 12$$

then capital Ratio = $$ \dfrac {15}{2} \times 3 : 30x \times 3 : 9x \times 12 $$

$$ \Rightarrow \dfrac {15}{2}: 30 : 9 \times 4 $$

$$\Rightarrow 15 : 60 : 72 $$

Let total profit = P As profit share = Rs 24000 

Capital ratio = profit ratio = 15:60 : 72 

$$ P \times \dfrac {15}{15+60+72} = 24000 $$

$$\Rightarrow P \times \dfrac {15}{147} = 24000 $$

$$\Rightarrow P = \dfrac {24000\times 147 } {15} $$

$$\Rightarrow P = 235200 $$

$$\Rightarrow total profit (P) = 235200$$ Ans