Question : A, B and C enter into a partnership with capitals in the ratio $\frac{2}{3}: \frac{3}{5}: \frac{5}{6}$. After 8 months, A increases his share of capital by 25%. If at the end of the year, the total profit earned is INR 5,820, then the share of C in the profit is:
Option 1: INR 2,050
Option 2: INR 2,350
Option 3: INR 2,450
Option 4: INR 2,250
Correct Answer: INR 2,250
Solution :
Capitals ratio of A, B and C
= $\frac{2}{3} : \frac{3}{5} : \frac{5}{6}$
= $\frac{2\times30}{3} : \frac{3\times30}{5} : \frac{5\times30}{6}$
= $20 : 18 : 25$
Capitals ratio of A, B and C after the end of the year,
$=(20 × 8 + 20 × \frac{5}{4} × 4) : 18 × 12 : 25 × 12$
$=(160 + 100) : 216 : 300$
$=260 : 216 : 300$
Capitals ratio of A, B and C after end of the year $=260x : 216x : 300x = 65x : 54x : 75x$
According to the question,
$65x + 54x + 75x = 5820$
⇒ $194x = 5820$
⇒ $x = 30$
$\therefore$ Share of C = 75 × 30 = INR 2,250
Hence, the correct answer is INR 2,250.
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