A natural number, when increased by 12, equals 160 times its reciprocal. Such a number is 8.

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A natural number, when increased by 12, equals 160 times its reciprocal. Such a number is 8.

A. True
B. False

Answer (A) True

Explain:-

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Given, a natural number increased by 12 equals to 160 times its reciprocal.

We have to find the natural number.

Let the natural number be x.

So, x + 12 = 160(1/x)

On rearranging,

x² + 12x = 160
x² + 12x – 160 = 0

On factoring,

x² + 20x – 8x – 160 = 0
x(x + 20) – 8(x + 20) = 0
(x – 8)(x + 20) = 0

Now, x – 8 = 0

x = 8

Also, x + 20 = 0

x = -20

Since a negative number cannot be negative, x = -20 is neglected.

Therefore, the natural number is x = 8.


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