Question

Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer.

What is the amount received by Shimona?

I. Samarth and Shimona started a business with an investment in the ratio of 5 ∶ 4. After 4 months Sujoy joined their business with an amount 20% more than that of Samarth after 2 more months Shimona took out 25% of her investment. The total profit obtained after the end of year is Rs.25000.

II. Samarth invested Rs.7000 more than that of Shimona. Sujoy invested 9000 more than Samarth and the difference between the profit earned by them is Rs.2000.

1. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
2. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
3. If the data either in statement I alone or in statement II alone is sufficient to answer the question.
4. If the data even in both the statements I and II together are not sufficient to answer the question.
5. If the data in both statements I and II together are needed to answer the question.

Answer 1

Correct Answer - Option 1 : If the data in statement I alone is sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

Using statement I

The investment of Samarth and Shimona is in ratio 5 ∶ 4

⇒ Let the investment of Samarth and Shimona be 5x and 4x respectively

Sujoy invested 20% more than that invested by Samarth 

⇒ Investment of Sujoy = (120/100) × 5x = 6x

∴ Profit weightage of Samarth = 5x × 12 = 60x

Profit weightage of Shimona = 4x × 6 + (4x × 75/100) × 6  = 24x + 18x = 42x

Profit weightage of Sujoy = (5x × 120/100) × 8 = 48x

Ratio of profit = 60x ∶ 42x ∶ 48x

⇒ Ratio = 10 ∶ 7 ∶ 8

Total profit = Rs.25,000 

∴ Amount earned by Shimona = (7/25) × 25,000 = Rs.7000

Statement I alone is sufficient to answer the question

 

Using statement II

Samarth invested Rs.9000 more than that of Shimona

⇒ Let the amount invested by Shimona be x

Then, the amount invested by Samarth = x + 7000 

Amount invested by Sujoy = x + 16000 

The difference between the profit earned by them is Rs.2000

Statement II alone is not sufficient to answer the question 

∴ The data in statement I alone is sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.