Ratio, Proportion, Indices, LogarithmMCQPYQ June 22Question 803 of 302
All Questions

A box contains $25$ paise coins and $10$ paise coins and 5\displaystyle 5 paise coins in ratios $3:2:1$ and total money is $₹40$. How many $5$ paise coins are there?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — $40$

All Options:

  • A$65$
  • B$55$
  • C$40$
  • D$50$

Detailed Solution & Explanation

Let the number of coins of 25 paise, 10 paise, and 5 paise be represented as $3x\displaystyle , &#36;2x, and $1xrespectively.<br>Themonetaryvaluesofthecoinsare\displaystyle respectively.<br>The monetary values of the coins are₹0.25,\displaystyle ,₹0.10,and\displaystyle , and₹0.05respectively.<br>Thetotalmoneyintheboxis\displaystyle respectively.<br>The total money in the box is₹40:<br><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mn>3</mn><mi>x</mi><mostretchy="false">(</mo><mn>0.25</mn><mostretchy="false">)</mo><mo>+</mo><mn>2</mn><mi>x</mi><mostretchy="false">(</mo><mn>0.10</mn><mostretchy="false">)</mo><mo>+</mo><mi>x</mi><mostretchy="false">(</mo><mn>0.05</mn><mostretchy="false">)</mo><mo>=</mo><mn>40</mn></mrow><annotationencoding="application/x−tex">3x(0.25)+2x(0.10)+x(0.05)=40</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">3</span><spanclass="mordmathnormal">x</span><spanclass="mopen">(</span><spanclass="mord">0.25</span><spanclass="mclose">)</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">2</span><spanclass="mordmathnormal">x</span><spanclass="mopen">(</span><spanclass="mord">0.10</span><spanclass="mclose">)</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mordmathnormal">x</span><spanclass="mopen">(</span><spanclass="mord">0.05</span><spanclass="mclose">)</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">40</span></span></span></span></span><br><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mn>0.75</mn><mi>x</mi><mo>+</mo><mn>0.20</mn><mi>x</mi><mo>+</mo><mn>0.05</mn><mi>x</mi><mo>=</mo><mn>40</mn></mrow><annotationencoding="application/x−tex">0.75x+0.20x+0.05x=40</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">0.75</span><spanclass="mordmathnormal">x</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">0.20</span><spanclass="mordmathnormal">x</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">0.05</span><spanclass="mordmathnormal">x</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">40</span></span></span></span></span><br><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mn>1.00</mn><mi>x</mi><mo>=</mo><mn>40</mn><mtext>  </mtext><mo>⟹</mo><mtext>  </mtext><mi>x</mi><mo>=</mo><mn>40</mn></mrow><annotationencoding="application/x−tex">1.00x=40  ⟹  x=40</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">1.00</span><spanclass="mordmathnormal">x</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6684em;vertical−align:−0.024em;"></span><spanclass="mord">40</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">⟹</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.4306em;"></span><spanclass="mordmathnormal">x</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">40</span></span></span></span></span><br>Thenumberof5paisecoinsintheboxis\displaystyle :<br><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>3</mn><mi>x</mi><mo stretchy="false">(</mo><mn>0.25</mn><mo stretchy="false">)</mo><mo>+</mo><mn>2</mn><mi>x</mi><mo stretchy="false">(</mo><mn>0.10</mn><mo stretchy="false">)</mo><mo>+</mo><mi>x</mi><mo stretchy="false">(</mo><mn>0.05</mn><mo stretchy="false">)</mo><mo>=</mo><mn>40</mn></mrow><annotation encoding="application/x-tex">3x(0.25) + 2x(0.10) + x(0.05) = 40</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">3</span><span class="mord mathnormal">x</span><span class="mopen">(</span><span class="mord">0.25</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mord mathnormal">x</span><span class="mopen">(</span><span class="mord">0.10</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">x</span><span class="mopen">(</span><span class="mord">0.05</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">40</span></span></span></span></span><br><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>0.75</mn><mi>x</mi><mo>+</mo><mn>0.20</mn><mi>x</mi><mo>+</mo><mn>0.05</mn><mi>x</mi><mo>=</mo><mn>40</mn></mrow><annotation encoding="application/x-tex">0.75x + 0.20x + 0.05x = 40</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">0.75</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">0.20</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0.05</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">40</span></span></span></span></span><br><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>1.00</mn><mi>x</mi><mo>=</mo><mn>40</mn><mtext>  </mtext><mo>⟹</mo><mtext>  </mtext><mi>x</mi><mo>=</mo><mn>40</mn></mrow><annotation encoding="application/x-tex">1.00x = 40 \implies x = 40</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1.00</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6684em;vertical-align:-0.024em;"></span><span class="mord">40</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⟹</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">40</span></span></span></span></span><br>The number of 5 paise coins in the box isx = 40$.

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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