Question

A natural number, when increased by 12, equals 160 times its reciprocal. Find the number

NCERT Class X
Mathematics - Exemplar Problems

Chapter _QUADRATIC EQUATIONS

Answer 1

Let the number be x,
ATQ ,   x +12 = 160/x
= x(x+12) = 160
= x² + 12x - 160 = 0
= x² + 20x - 8x - 160 = 0
= x(x+20) - 8(x+20) = 0
= (x-8)(x+20) = 0

Therefore, x is equal to -20 and 8.
Now, as the question says that x is a natural number, it can't be negative.
Thus, x = 8

Hope that helps !!

Answer 2

Let the number be x 
Given that , x +12 = 160/x
               ⇒x²+12x-160 = 0 
               ⇒x²+20x-8x-160 = 0 
               ⇒x(x+20) -8(x+20) 
               ⇒(x-8)(x+20) = 0 
        ⇒(x-8) = 0 , (x+20) = 0 
        ⇒ x = 8 , x = -20 .
Given that , x is a natural number . So , it can't be negative .
⇒ x = 8 .