Question

Ankit, Ashish and Arun earned a profit of Rs. 12 lakh from a year from their business. Ankit retained Rs. 6 lakh, while Ashish and Arun each kept Rs. 3 lakh. What is the ratio of their profits from the business?

• A. 3:1:2
• B. 2:1:1
• C. 3:1:1
• D. 4:1:2

Hint:

Write the three shares as 6 : 3 : 3 and divide each term by their common factor 3.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The total profit is Rs. 12 lakh. It is shared among three people, and the share of each person is given directly. We only need to write the three shares as a ratio and simplify it.

Step 2: Key Formula or Approach:
A ratio compares amounts of the same kind. To simplify it, divide every term by the same common factor.
\[ \text{Ratio} = \text{Ankit} : \text{Ashish} : \text{Arun} \]

Step 3: Write the shares:
Ankit kept Rs. 6 lakh. Ashish kept Rs. 3 lakh. Arun kept Rs. 3 lakh.
Check: \(6 + 3 + 3 = 12\), which matches the total profit.
So the ratio is \(6 : 3 : 3\).

Step 4: Simplify the ratio:
The highest common factor of 6, 3 and 3 is 3. Divide each term by 3.
\[ 6 : 3 : 3 = \frac{6}{3} : \frac{3}{3} : \frac{3}{3} = 2 : 1 : 1 \]

Step 5: Check option (1) 3:1:2:
This option gives Arun double the share of Ashish. But Ashish and Arun kept equal amounts. So option (1) is wrong.

Step 6: Check options (3) and (4):
Option (3) 3:1:1 makes Ankit's share 3 times Ashish's share, but it is only 2 times (6 against 3). Option (4) 4:1:2 makes Arun's share double Ashish's, but they are equal. So both are wrong.

Final Answer:
The ratio of the profits of Ankit, Ashish and Arun is 2:1:1. This is option (2). \[ \boxed{2:1:1} \]