Ratio, Proportion, Indices, LogarithmsPYQ Sept 25Question 4401 of 220
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XYZ invested ₹ 1,68,000 in a business. After a few months, MNP joined in the business by investing ₹ 1,12,000 in the business. At the end of year, the total profit was divided between them in the ratio 2:1. After how many months, did MNP join the business?

Options

A3
B2
C4
D9
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Correct Answer

✅ Option a — 3

All Options:

  • A3
  • B2
  • C4
  • D9

Detailed Solution & Explanation

Let the investment duration of XYZ be 12 months (1 year). Let the investment duration of MNP be t\displaystyle t months.
The profit is divided in the ratio of the product of their investments and their respective time periods: Profit of XYZ:Profit of MNP=(Investment of XYZ×12):(Investment of MNP×t)\text{Profit of XYZ} : \text{Profit of MNP} = (\text{Investment of XYZ} \times 12) : (\text{Investment of MNP} \times t)
Substitute the given values: Ratio=1,68,000×121,12,000×t=21\text{Ratio} = \frac{1,68,000 \times 12}{1,12,000 \times t} = \frac{2}{1}
Simplifying the investment ratio: 168×12112×t=2\frac{168 \times 12}{112 \times t} = 2
Since 168=56×3\displaystyle 168 = 56 \times 3 and 112=56×2\displaystyle 112 = 56 \times 2: 3×122×t=2\frac{3 \times 12}{2 \times t} = 2 362t=2\frac{36}{2t} = 2 18t=2  ⟹  2t=18  ⟹  t=9 months\frac{18}{t} = 2 \implies 2t = 18 \implies t = 9\text{ months}
MNP was in the business for 9 months. The number of months after which MNP joined the business is: Months elapsed=12−9=3 months\text{Months elapsed} = 12 - 9 = 3\text{ months}
Hence, **Option A** is the correct answer.

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