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<html><body><h2 id="content-id-3549207186-2"><b>Number System Questions Overview</b></h2><p>Number System Questions have a good weightage in the SSC CHSL English Exam and the type of question asked in SSC CHSL English exam is similar to the question mentioned below. It has been solved and explained by KD Live Experts under the guidance of Neetu Mam and they have tried to elaborate the concept used in Number System Questions.</p><h2 id="content-id-5432198706-3"><b>Question On Number System </b></h2>The sum of three numbers is 80 and the sum of the squares of these three numbers is 2,650. If the product of the three numbers is 13,500, then find the sum of the cubes of the given three numbers.
<div class="row show--dificulty--bar" style="margin-top:8px;"><div class="col-sm-6 show--dificulty--bar" style="display:inline-flex !important;border-right:0.1px solid #eee;"><h3 style="font-size:12px !important;">Difficulty : Easy </h3></div><div class="col-sm-6 show--dificulty--bar" style="display:inline-flex;"><h3 style="font-size:12px !important;"> Average Time : 37 Seconds </h3></div></div><h2 id="content-id-1784296350-4"><b> Number System Questions Options</b></h2><ol><li><p>1,46,580</p>
</li><li><p>87,860</p>
</li><li><p>1,90,750</p>
</li><li><p>1,02,500</p>
</li></ol> <h2 id="content-id-1639280745-5"><b> Number System Questions Solution</b></h2><p>The correct answer is <strong>Option 4</strong> i.e. <strong>1,02,500.</strong></p>

<p>Let the three numbers be a, b, and c.</p>

<p>a + b + c = 80 ...(1)</p>

<p>a<sup>2</sup> + b<sup>2</sup> + c<sup>2</sup> = 2650 ...(2)</p>

<p>abc = 13500 ...(3)</p>

<p>(a + b + c)<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup> + c<sup>2</sup> + 2(ab + bc + ca)</p>

<p>⇒ 80<sup>2</sup> = 2650 + 2(ab + bc + ca)</p>

<p>⇒ 6400 = 2650 + 2(ab + bc + ca)</p>

<p>⇒ 2(ab + bc + ca) = 6400 - 2650 = 3750</p>

<p>⇒ ab + bc + ca = 3750/2 = 1875</p>

<p>a<sup>3</sup> + b<sup>3</sup> + c<sup>3</sup> – 3abc = (a + b + c)(a<sup>2</sup> + b<sup>2</sup> + c<sup>2</sup> – ab – bc – ca)</p>

<p>⇒ a<sup>3</sup> + b<sup>3</sup> + c<sup>3</sup> – 3 × 13500 = 80(2650 – 1875) = 80 × 775 = 62000</p>

<p>⇒ a<sup>3</sup> + b<sup>3</sup> + c<sup>3</sup> – 40500 = 62000</p>

<p>⇒ a<sup>3</sup> + b<sup>3</sup> + c<sup>3</sup> = 62000 + 40500 = 102500</p>
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The correct answer is Option 4 i.e. 1, - Number System Questions are asked in SSC CHSL English exams and your question has been explained by experts like Neetu Mam.

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