A invested Rs 2400 in a partnership business, and after 8 months, B joined the business with an amount of Rs X. At the end of the year, the profit of B is 3/11 of the total profit. Find the value of X (in Rs).

​​​Information Given in the Question:

A invested = Rs 2400
A invested for = 12 months

B joined after = 8 months

So, B invested for = 4 months

Profit of B = 3/11 of total profit

Concept/Formula Used in the Question:
In partnership business,

Profit ∝ Investment × Time

So,

Profit ratio = (Investment × Time)

Investment-time of A
= 2400 × 12
= 28800

Investment-time of B
= X × 4
= 4X

Since B's profit = 3/11 of total profit

So profit ratio of B : A

= 3 : 8

Now,

​$$\frac{4x}{28800} = \frac{3}{8}$$​​

4X × 8 = 28800 × 3

32X = 86400

X =$$\frac{86400}{32}$$​​

X = 2700