Ratio, Proportion, Indices, LogarithmsPYQ May 25Question 4000 of 220
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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

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.

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