Ratio, Proportion, Indices, LogarithmMCQPYQ May 25Question 4300 of 305
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A startup business was initiated by an entrepreneur by investing ₹ 1,40,000. His friend joined him after six months with an amount of ₹ 2,10,000. Thereafter an angel investor joined them with ₹ 2,80,000 after another six months. What should be the ratio of distribution of total earnings, three years since beginning of business among entrepreneur, his friend and angel investor?

Options

A7:6:10
B12:15:16
C42:45:56
D2:3:4
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Correct Answer

✅ Option b — 12:15:16

All Options:

  • A7:6:10
  • B12:15:16
  • C42:45:56
  • D2:3:4

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Detailed Solution & Explanation

To find the ratio of distribution of total earnings, we need to calculate the ratio of the product of the investment and the duration of the investment for each person.
Let the duration of the business be 3 years, which is equivalent to 36 months.
1. **Entrepreneur's investment details**:
Investment amount = ₹1,40,000\displaystyle ₹ 1,40,000
Duration = 36 months\displaystyle 36 \text{ months}
Product of investment and time = 1,40,000×36\displaystyle 1,40,000 \times 36

2. **Friend's investment details**:
The friend joined after 6 months. Therefore, the duration of the investment is:
36−6=30 months36 - 6 = 30 \text{ months}
Investment amount = ₹2,10,000\displaystyle ₹ 2,10,000
Product of investment and time = 2,10,000×30\displaystyle 2,10,000 \times 30

3. **Angel Investor's investment details**:
The angel investor joined after another 6 months (i.e., 12 months from the beginning). Therefore, the duration of the investment is:
36−12=24 months36 - 12 = 24 \text{ months}
Investment amount = ₹2,80,000\displaystyle ₹ 2,80,000
Product of investment and time = 2,80,000×24\displaystyle 2,80,000 \times 24

Now, let's find the ratio of distribution of earnings:
Ratio=(1,40,000×36):(2,10,000×30):(2,80,000×24)\text{Ratio} = (1,40,000 \times 36) : (2,10,000 \times 30) : (2,80,000 \times 24)
Dividing each term by 10,000\displaystyle 10,000, we get:
(14×36):(21×30):(28×24)(14 \times 36) : (21 \times 30) : (28 \times 24)
Dividing by 7\displaystyle 7 (since 14\displaystyle 14, 21\displaystyle 21, and 28\displaystyle 28 are multiples of 7\displaystyle 7):
(2×36):(3×30):(4×24)(2 \times 36) : (3 \times 30) : (4 \times 24)
=72:90:96= 72 : 90 : 96
Dividing by 6\displaystyle 6 to simplify to the lowest terms:
726:906:966=12:15:16\frac{72}{6} : \frac{90}{6} : \frac{96}{6} = 12 : 15 : 16
Hence, **Option B** is the correct answer.

About This Chapter: Ratio, Proportion, Indices, Logarithm

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Ratio, Proportion, Indices, Logarithms

This chapter covers Ratio, Proportion, Indices, Logarithms and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5-7 Marks weightage. Focus on understanding core concepts rather than memorizing.

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