$A$ starts a business with $Rs. 4000$ and $B$ joins him after $3$ months with $Rs. 16000$. Find the ratio of their profits at the end of the year.

Simran started a software business by investing ₹ $50000$. After six months,Nanda joined her with a capital of ₹ $80000$. After $3$ years,they earned a profit of ₹ $24500$. What was Simran's share in the profit? (In ₹)

$A$ and $B$ started a partnership business by investing in the ratio of $3:8$. $C$ joined them after $4$ months with an amount equal to $\frac{3}{4}$ of $B$'s investment. What was the total profit (in ₹) at the end of the year if $C$ received ₹ $24000$ as his share?

$A, B$ and $C$ entered into a partnership in the ratio $\frac{7}{2}: \frac{4}{3}: \frac{6}{5}$. After $4$ months,$A$ increases his share by $50\%$. If the total profit at the end of one year is ₹ $21600$,then find $B$'s share in the profit (in ₹).

$A$ and $B$ jointly invest ₹ $2100$ and ₹ $3100$ in a firm. $A$ is an active partner,hence he receives $25 \%$ of the profit separately. If their business yields ₹ $1040$ as profit,what will be the profit share for each of them?

Gupta and Bansal enter into a partnership with their capitals in the ratio $5:6$. At the end of $8$ months,Gupta withdraws his capital. If they receive their shares of profits in the ratio of $5:9$,find out how long (in months) Bansal's capital was invested in the business?