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

Solution:

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.

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

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4

NCERT Exemplar Class 10 Maths Exercise 4.4 Problem 3

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

Summary:

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

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