Three persons A, B and C enter into a partnership to run a business. They invested their capitals in the ratio $\frac{4}{3}:\frac{5}{2}:\frac{6}{5}.$ After 5 months B increases his share by 40%. If the total profit at the end of a year is ₹50,550, then A's share in the profit is :

₹12,000

The correct answer is Option (2) → ₹12,000

The initial investment ratio of A, B and C is,

$A : B : C = 45 : 52 : 65$

Let their initial investment

$A = 43x, B = 52x, C = 65x$

A and C kept their investment.

B increased his investment = $52x+40\%\,of\,52x=72.8x$

Total capital for each person,

$A=43x×12=516x$

$B=(52x×5)+(72.8x×7)=769.6x$

$C=(65x×12)=780x$

$A : B : C = 516: 769.6 : 780$

Total profit = 50,550

A's share = $\frac{516}{2065.6}×50,550$

$≃₹12,000$