A, B and C 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 ₹)?

₹2,35,200

Let  capital of A = 4x

Let capital of B = 2x

Let capital of C = 9x

 Total capital of A after end of the year = 4x × 3 + \(\frac{4x}{2}\) × 3 + \(\frac{4x}{2}\) × 3 +\(\frac{4x}{8}\) × 3

= 12x + 6x + 3x + \(\frac{3x}{2}\) = \(\frac{45x}{2}\)

 Total capital of B after end of the year = 2x × 3 + 4x × 3 + 8x × 3 + 16x×3

= (6 + 12 + 24 + 48)x

= 90x

 Total capital of C after end of the year = 9x × 12 = 108x

 Profit ratio of A, B and C =

(45/2) : 90 : 108 

    5    : 20   : 24

 5x = 24000

 1x = (\frac{2400}{5}\)= 4800

Total profit = (5 + 20 + 24)x = 49x

= 4800 × 49

= Rs. 235200