Question

Sachin invested Rs. 95,000 in a business. After a few months, Viju joined him with Rs. 57,000. At the end of the year, the total profit was divided between them in the ratio 2:1. After how many months did Viju join?

• A. 2
• B. 5
• C. 4
• D. 3
• E.

Hint:

When calculating the time an investor joins, use the ratio of investments and profit to set up equations and solve for the unknown.

Answer 1

The Correct Option is A

Let Sachin invest Rs. 95,000 for a duration of 12 months. Let Viju join after \( x \) months. Step 1: Expressing the Investments
- Sachin’s total investment is: \[ 95,000 \times 12 \] - Viju’s total investment is: \[ 57,000 \times (12 - x) \] Step 2: Setting Up the Ratio
The profit is divided in the ratio 2:1, meaning the ratio of their investments must be: \[ \frac{95,000 \times 12}{57,000 \times (12 - x)} = 2 \] Step 3: Simplifying the Equation
\[ \frac{12}{12 - x} = \frac{2 \times 57,000}{95,000} \] \[ = \frac{114,000}{95,000} = \frac{12}{10} = 1.2 \] \[ \frac{12}{12 - x} = 1.2 \] Step 4: Solving for \( x \)
\[ 12 = 1.2 \times (12 - x) \] \[ 12 = 14.4 - 1.2x \] \[ 1.2x = 2.4 \] \[ x = \frac{2.4}{1.2} = 2 \] Thus, Viju joined after 2 months.