Ratio, Proportion, Indices, LogarithmMCQMTP June 22Question 838 of 305
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X,Y,Z\displaystyle X, Y, Z together starts a business, if X\displaystyle X invests 3\displaystyle 3 times as much as Y\displaystyle Y invests and Y\displaystyle Y invests two third of what Z\displaystyle Z invests, then the ratio of capitals of X,Y,Z\displaystyle X, Y, Z is

Options

A3:9:2\displaystyle 3:9:2
B6:3:2\displaystyle 6:3:2
C3:6:2\displaystyle 3:6:2
D6:2:3\displaystyle 6:2:3
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Correct Answer

✅ Option d — 6:2:3\displaystyle 6:2:3

All Options:

  • A3:9:2\displaystyle 3:9:2
  • B6:3:2\displaystyle 6:3:2
  • C3:6:2\displaystyle 3:6:2
  • D6:2:3\displaystyle 6:2:3

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Detailed Solution & Explanation

Let CX\displaystyle C_X, CY\displaystyle C_Y, and CZ\displaystyle C_Z be the capitals invested by X\displaystyle X, Y\displaystyle Y, and Z\displaystyle Z respectively. From the problem statement, we are given two relationships between their investments: **1. Relationship between X\displaystyle X's and Y\displaystyle Y's investment:** "X\displaystyle X invests 3\displaystyle 3 times as much as Y\displaystyle Y invests" This can be mathematically expressed as: CX=3×CYC_X = 3 \times C_Y CX=3CY(Equation 1)C_X = 3C_Y \quad \text{(Equation 1)} **2. Relationship between Y\displaystyle Y's and Z\displaystyle Z's investment:** "Y\displaystyle Y invests two third of what Z\displaystyle Z invests" This can be mathematically expressed as: CY=23×CZC_Y = \frac{2}{3} \times C_Z CY=23CZ(Equation 2)C_Y = \frac{2}{3}C_Z \quad \text{(Equation 2)} Our objective is to find the ratio of capitals CX:CY:CZ\displaystyle C_X : C_Y : C_Z. To do this, we need to express all capitals in terms of a single variable. Let's express CX\displaystyle C_X and CY\displaystyle C_Y in terms of CZ\displaystyle C_Z. From Equation 2, we already have CY\displaystyle C_Y in terms of CZ\displaystyle C_Z: CY=23CZC_Y = \frac{2}{3}C_Z Now, substitute this expression for CY\displaystyle C_Y into Equation 1 to find CX\displaystyle C_X in terms of CZ\displaystyle C_Z: CX=3CYC_X = 3C_Y Substitute $C_Y = \frac{2

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.

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Exam Strategy Tip

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

More Questions from Ratio, Proportion, Indices, Logarithm

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If the ratio of two numbers is 7:11\displaystyle 7:11. If 7\displaystyle 7 is added to each number then the new ratio will be 2:3\displaystyle 2:3 then the numbers are.

If x:y=z:7=4:11\displaystyle x:y=z:7=4:11 then x+y+zz\displaystyle \frac{x+y+z}{z} is

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The price of scooter and moped are in the ratio 7:9\displaystyle 7:9. The price of moped is ₹1,600\displaystyle ₹1,600 more than that of scooter. Then the price of moped is:

If A:B=3:7\displaystyle A:B=3:7, then 3a+2b:4a+5b=?\displaystyle 3a+2b:4a+5b=?

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