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Question
A natural number when increased by 12, equals 160 times reciprocal. The number is-
16
8
6
18
ANSWER : 2
Descrption
<p>Step 1: Construct the equation based on given condition.<br>let the required natural number be x.<br>According to the question,<br>x+12=160/x<br>On multiplying by x on both sides, we get<br>x^2+12x−160=0,<br><br>step 2: Find roots using factorization.<br>By splitting the middle term, we get :<br>⇒x^2+(20x−8x)−160=0<br>⇒x^2+20x−8x−160=0<br>⇒x(x+20)−8(x+20)=0<br>⇒(x+20)(x−8)=0<br>⇒x=8<br>[x≠−20 because it is not a natural number]<br>hence, the required natural number is 8<br> </p>
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