Ratio, Proportion, Indices, LogarithmMCQPYQ June 22Question 885 of 305
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The value of (1−0.0273(56)(12)2)\displaystyle \left(1-\sqrt[3]{0.027}\left(\frac{5}{6}\right)\left(\frac{1}{2}\right)^2\right) is

Options

A1116\displaystyle \frac{11}{16}
B1316\displaystyle \frac{13}{16}
C1516\displaystyle \frac{15}{16}
D1
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Correct Answer

✅ Option c — 1516\displaystyle \frac{15}{16}

All Options:

  • A1116\displaystyle \frac{11}{16}
  • B1316\displaystyle \frac{13}{16}
  • C1516\displaystyle \frac{15}{16}
  • D1

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Detailed Solution & Explanation

We want to evaluate the expression:
1−0.0273×(56)×(12)21 - \sqrt[3]{0.027} \times \left(\frac{5}{6}\right) \times \left(\frac{1}{2}\right)^2
Let us simplify each term step by step:
1. Simplify the cube root:
0.027=271000=(310)30.027 = \frac{27}{1000} = \left(\frac{3}{10}\right)^3
0.0273=310=0.3\sqrt[3]{0.027} = \frac{3}{10} = 0.3
2. Simplify the square term:
(12)2=14\left(\frac{1}{2}\right)^2 = \frac{1}{4}
3. Substitute these values back into the expression:
1−(310)×(56)×(14)1 - \left(\frac{3}{10}\right) \times \left(\frac{5}{6}\right) \times \left(\frac{1}{4}\right)
4. Calculate the product:
3×5×110×6×4=15240\frac{3 \times 5 \times 1}{10 \times 6 \times 4} = \frac{15}{240}
Dividing the numerator and denominator by 15\displaystyle 15:
15240=116\frac{15}{240} = \frac{1}{16}
5. Subtract the product from 1\displaystyle 1:
1−116=15161 - \frac{1}{16} = \frac{15}{16}
This mathematically corresponds to **Option C**.
Note: The textbook answer key incorrectly specifies **Option A** (1116\displaystyle \frac{11}{16}) as correct. However, our step-by-step arithmetic proof shows the correct answer must be 1516\displaystyle \frac{15}{16} (Option C).
Hence, **Option C** 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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