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

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Sum

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

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Solution

Let the natural number = x

When the number increased by 12 = x + 12

Reciprocal of the number = `1/x`

We have

x + 12 = 160 times of reciprocal of x

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 + 20)(x – 8) = 0

x + 20 = 0 or x – 8 = 0

x = – 20 or x = 8

Since, natural numbers cannot be negative.

The required number = x = 8

Concept: Nature of Roots
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APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 4 Quadatric Euation
Exercise 4.4 | Q 3 | Page 42
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