Ratio, Proportion, Indices, LogarithmMCQMTP June 2023 Series IQuestion 843 of 305
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Four persons A,B,C,D\displaystyle A, B, C, D wish to share a sum in the ratio of 5:2:4:3\displaystyle 5:2:4:3. If D\displaystyle D gets Rs.1000\displaystyle \text{Rs.} 1000 less than C\displaystyle C, then the share of B\displaystyle B?

Options

A2000\displaystyle 2000
B1200\displaystyle 1200
C2400\displaystyle 2400
D3000\displaystyle 3000
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Correct Answer

✅ Option a — 2000\displaystyle 2000

All Options:

  • A2000\displaystyle 2000
  • B1200\displaystyle 1200
  • C2400\displaystyle 2400
  • D3000\displaystyle 3000

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Detailed Solution & Explanation

Let the sum be shared by A,B,C,D\displaystyle A, B, C, D in the ratio 5:2:4:3\displaystyle 5:2:4:3.
To represent their individual shares, we introduce a common positive constant, say k\displaystyle k.
Then, the shares of A,B,C,D\displaystyle A, B, C, D can be expressed as:
Share of A=5k\displaystyle A = 5k
Share of B=2k\displaystyle B = 2k
Share of C=4k\displaystyle C = 4k
Share of D=3k\displaystyle D = 3k
We are given the condition that D\displaystyle D gets Rs.1000\displaystyle \text{Rs.} 1000 less than C\displaystyle C.
This can be mathematically expressed as: Share of D=Share of C−1000\text{Share of } D = \text{Share of } C - 1000 Now, substitute the expressions for the shares of C\displaystyle C and D\displaystyle D in terms of k\displaystyle k into this equation: 3k=4k−10003k = 4k - 1000 To solve for k\displaystyle k, we rearrange the equation: 1000=4k−3k1000 = 4k - 3k 1000=k1000 = k Thus, the value of the common constant k\displaystyle k is 1000\displaystyle 1000.
The question asks for the share of B\displaystyle B.
From our initial definitions, the share of B\displaystyle B is 2k\displaystyle 2k.
Substitute the value of k=1000\displaystyle k = 1000 into the expression for B\displaystyle B's share: Share of B=2×1000\text{Share of } B = 2 \times 1000 Share of B=2000\text{Share of } B = 2000 Therefore, the share of B\displaystyle B is Rs.2000\displaystyle \text{Rs.} 2000.
Comparing this result with the given options, we find that it matches Option A. Hence, **Option A** 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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