One of the topic which frequently appears in mocks. This is pretty straightforward topic and is dependent basically on two quantities :
1. Amount Invested (P)
2. Time of investment (t)
The ratio of product of these two for each is basically the ratio in which profit is divided.
So profit ratio is P*t ratio of each.

Enough of theory, let’s deal with few Qs to get better understanding.

Q. A and B invested Rs. 2000 and Rs. 3000 respectively in some business. At the end of the year they made a profit of Rs. 1500.  What is A’s share of profit?

Solution .

Investment Ratio
A: B
= 2000:3000
= 2:3

Time ratio
A:B
= 12:12(Number of months)
= 1:1

The ratio in which profit is divided is basically product of the two-investment and time:
So profit ratio of A and B is:
= 2*1:3*1
= 2:3

So 1500 will be divided in 2:3

Therefore A gets (2/(2+3))*1500=600
B gets (3/(2+3))*1500=900

Hence 600 is the answer.

 

Q. Raman(R) and Sarita(S) invested capital in the ratio 8 : 9. The time Sarita invested her money was two years more than that invested By Raman. The ratio of their profits is 8 : 15. Find the time for which Sarita invested her money.

Solution .
Investment ratio
R:S
= 8:9

Time ratio
R:S
= t:(t+2)

Profit ratio
R:S
= 8:15

Ratio of Product of investment and time is the ratio of profit.

So
8t/9(t+2)=8/15
15t=9t+18
t=3 is the time for Raman
S=t+2=5 ans

 

One more variety of Qs also appears:

When one of the partner is sleeping partner and other is working.
(Sleeping partner : Just invests and works nothing in the business.
Working partner: Invests as well as manages the business.)
In such cases usually working partner , apart from the profit ratio, takes some more amount for managing the business as well.
Let’s get this with an example.

Q. Arun(A) started a business with Rs 52000 and after four months, Varoon(V) joined with Rs. 39,000. At the end of the year out of the total profit, Varoon received total Rs. 20,000 in adding one fourth of the profits as commission for managing the business. What profit did Arun receive?

Solution :
Amount invested ratio :
A:V
=52000:39000
=4:3

Time ratio
A:V
=12:8
=3:2

Ratio in which the profit will be divided:
A:V
= 4*3:3*2
= 12:6
= 2:1

But here is the involvement of working partner concept
V is the working partner, as he manages the business.

So say total profit is 4x,
Varoon apart from profit ratio receives for managing business receives and that is equal to one-fourth of the total profit
so 4x/4=x

Remaining profit is distributed as per Investment * Time ratio

Remaining profit =4x-x=3x

A:V investment*time ratio is 2:1
So A gets 2x and V gets x

V in total gets :
=x(for managing business )+x (for the investment *time )
=2x

And this 2x in the question is given as 20000.

Also Arun receives 2x as profit
So Arun also gets 2x=20000 ans