Ratio, Proportion, Indices, LogarithmMCQPYQ Dec 22Question 805 of 302
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A group of $400$ soldiers at border area had a provision for $31$ days. After $28\displaystyle days $280 soldiers from this group were called back. Find the number of days for which the remaining ration will be sufficient?

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

✅ Option d — $10$

All Options:

  • A3\displaystyle 3
  • B6\displaystyle 6
  • C8\displaystyle 8
  • D$10$

Detailed Solution & Explanation

A group of $400$ soldiers has provisions for $31$ days, which represents $400 ×\displaystyle \times 31 = 12,400\displaystyle soldier-days of ration.<br>After &#36;28 days, the ration consumed by the $400×\displaystyle \times …" style="color:#cc0000">\displaystyle soldiers is &#36;400 ×\displaystyle \times 28 = 11,200 soldier-days.
The remaining ration is:
Remaining Ration=12,400−11,200=400×(31−28)=1,200 soldier-daysRemaining Ration=12\displaystyle \text{Remaining Ration} = 12,400 - 11,200 = 400 ×\displaystyle \times (31 - 28) = 1,200  soldier-days\displaystyle \text{ soldier-days}
At this point, $280soldiersarecalledback.Theremainingnumberofsoldiersis:<br><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mtext>Remaining Soldiers</mtext><mo>=</mo><mn>400</mn><mo>−</mo><mn>280</mn><mo>=</mo><mn>120</mn><mtext> soldiers</mtext></mrow><annotationencoding="application/x−tex">Remaining Soldiers=400−280=120 soldiers</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.8889em;vertical−align:−0.1944em;"></span><spanclass="mordtext"><spanclass="mord">Remaining Soldiers</span></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:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">400</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">280</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:0.6944em;"></span><spanclass="mord">120</span><spanclass="mordtext"><spanclass="mord"> soldiers</span></span></span></span></span></span><br>Lettheremainingrationlastfor\displaystyle soldiers are called back. The remaining number of soldiers is:<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><mtext>Remaining Soldiers</mtext><mo>=</mo><mn>400</mn><mo>−</mo><mn>280</mn><mo>=</mo><mn>120</mn><mtext> soldiers</mtext></mrow><annotation encoding="application/x-tex">Remaining Soldiers=400−280=120\displaystyle \text{Remaining Soldiers} = 400 - 280 = 120  soldiers\displaystyle \text{ soldiers}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord text"><span class="mord">Remaining Soldiers</span></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:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">400</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">280</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:0.6944em;"></span><span class="mord">120</span><span class="mord text"><span class="mord"> soldiers</span></span></span></span></span></span><br>Let the remaining ration last forD$ days for the $120$ soldiers:
120×D=1,200  ⟹  D=10 days120 ×\displaystyle \times D = 1,200 \implies D = 10  days\displaystyle \text{ days}

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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