# Data Sufficiency

Partnership conditions are the terms under which a partnership is created. In partnerships, the questions from data sufficiency are a very common occurrence in the competitive exams. They can be asked from any chapters. And thus today our topic for data sufficiency will be on partnership conditions.

## Partnership conditions

We have covered several topics on partnerships in our previous articles. And so today we are going to show you to solve the questions based on partnership conditions in data sufficiency. So, we will look into some of the common questions asked under this section. Before solving the questions, here are the directions for the questions:

Each question given will be followed by two statements.

(a) if statement I alone is sufficient, but statement II alone is not sufficient.
(b) if statement II alone is sufficient, but the statement I alone is not sufficient.
(c) if both the statements I and II together are sufficient, but neither statements alone is sufficient.
(d) if each statement alone is sufficient.
(e) if statement I and II together are not sufficient.

Source: PxHere

### Examples:

Q. There were three friends named A, B, and C. They started their business together by investing the money in the ratio of 2: 5: 4 respectively. Furthermore, money was invested for a period of 3 years. If the total investment did is 33,000 rupees, what was the share of A in the overall profit made by them?

A. The average profit per year was Rs. 5500.
B. The profit made was 1/2 of the overall investment in three years.

Now, you have to find the share of A’s profit. You need to start the question by using statement I and statement II individually and then move on to solving the question by using both the statements together.

In statement I, it is given that the average profit per year was Rs. 5500. So, the total profit for three years will be (5500 x 3) = Rs. 16,500. While A’s share of the profit was 2/11. Thus, A’s profit will be 2/5 x 16500 = Rs. 3000. So, the total profit made by A was Rs. 3000 which is our required answer. So, we can find the answer using statement I alone.

We also need to find whether statement II alone is sufficient to answer the question. In statement II it is given that the total profit was 1/2th of the total investment. Here, the total investment is Rs. 33,000 so the total profit will be 1/2 x 33000 = Rs. 16,500. And as done in the above statement we will find the overall profit for A to be Rs. 3000.

So, both the statements in this question can individually solve this question. So the correct answer is option D.

### Examples with three statements

Q. Three friends named Ram, Shyam and Mukesh started a business together. What was Shyam’s overall profit at the end of the year?

The statement I: Mukesh invested Rs. 8000 for the 1st 9 months. Mukesh’s investment was 4 times as much as of Ram and 3/2 times that of Shyam.
Statement II: The investment done by Ram and Shyam was in the proportion of 1: 2 in one year.
Statement III: The total profit at the end of the year was Rs. 1000.

A. Only 1st and 2nd statement
B. Only 1st and 3rd statement
C. All of these
D. None of the statements
E. The information given in the statements is insufficient.

As there are three statements given in the question, we need to solve it on the basis of the options. So, on combining 1st and 2nd statement, we get,

Total money invested by Mukesh = (8000 x 9) = Rs. 72000.
Total money invested by Ram = (1/4 x 8000 x 12) = Rs. 24000
All the money invested by Shyam = (3/2 x 72000) = Rs. 48000

So, the ratio of the money invested by all of them will be 72000: 48000: 24000 = 3: 2: 1. So, we have found the ratio of each individual but we need to find the share of their profit. Thus, a statement I and II alone cannot be sufficient to determine the answer.

Furthermore, in the third statement, the total amount of profit is given. So, the share of Shyam’s profit will be (1/3 x 1000) = Rs. 333. 33.
So the correct answer is option D.

### Practice Questions:

Directions for the questions:
Each question given will be followed by two statements.

(a) if statement I alone is sufficient, but statement II alone is not sufficient.
(b) if statement II alone is sufficient, but the statement I alone is not sufficient.
(c) if both the statements I and II together are sufficient, but neither statements alone is sufficient.
(d) if each statement alone is sufficient.
(e) if statement I and II together are not sufficient.

Q. Three partners named X, Y, and Z decided to produce a movie. What will be the Y’s share of the profit earned by all of them?

The statement I: The share of Z in profit was Rs. 8750.
Statement II: The ratio of investment of X, Y, and Z was in the ratio of 2: 4: 7.

Q. The profit earned by the three partners at the end of 2 years was 30 %. If Mahesh, Suresh, and Vyomesh worked together, what was Suresh’s share of the profit?

The statement I: All the three members invested the amount of Rs. 25000 for two years.
Statement II: The total amount invested by Suresh was equal to the amount invested by Ramesh and Vyomesh.

Q. Sanjay started a business by investing Rs. 80,000. What was Vijay’s share of profit in the business?

The statement I: Vijay joined Sanjay:s business after 3 months.
Statement II: Ajay joined the business after 4 months and invested Rs. 1,20,000. His share of profit was Rs. 6000.

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