Ratio, Proportion, Indices, LogarithmMCQMTP Sep 24 Series IQuestion 869 of 305
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If 1/2,1/3,1/5\displaystyle 1/2, 1/3, 1/5 and 1/x\displaystyle 1/x are in proportion, then the value of x\displaystyle x will be

Options

A15/2\displaystyle 15/2
B5/6\displaystyle 5/6
C10/3\displaystyle 10/3
D5/6\displaystyle 5/6
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Correct Answer

✅ Option a — 15/2\displaystyle 15/2

All Options:

  • A15/2\displaystyle 15/2
  • B5/6\displaystyle 5/6
  • C10/3\displaystyle 10/3
  • D5/6\displaystyle 5/6

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Detailed Solution & Explanation

If four numbers A,B,C,D\displaystyle A, B, C, D are in proportion, then the ratio of the first two is equal to the ratio of the last two:
AB=CD\frac{A}{B} = \frac{C}{D}
Here, the four numbers are:
A=12,B=13,C=15,D=1xA = \frac{1}{2}, \quad B = \frac{1}{3}, \quad C = \frac{1}{5}, \quad D = \frac{1}{x}
Substitute these values into the proportion equation:
1213=151x\frac{\frac{1}{2}}{\frac{1}{3}} = \frac{\frac{1}{5}}{\frac{1}{x}}
Simplify both fractions:
- Left-hand side (LHS): 1213=12×3=32\displaystyle \frac{\frac{1}{2}}{\frac{1}{3}} = \frac{1}{2} \times 3 = \frac{3}{2}
- Right-hand side (RHS): 151x=15×x=x5\displaystyle \frac{\frac{1}{5}}{\frac{1}{x}} = \frac{1}{5} \times x = \frac{x}{5}
Now equate the LHS and RHS:
32=x5\frac{3}{2} = \frac{x}{5}
Solve for x\displaystyle x by multiplying both sides by 5\displaystyle 5:
x=3×52=152x = \frac{3 \times 5}{2} = \frac{15}{2}
This 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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