Question

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

Answer 1

❍ Let the natural number be x.

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★ According to given, x + 12 = 160/x

➺ x² + 12x = 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

〄 But x is a natural number, so we reject x = -20.

✿ Therefore,

• Hence, the required natural number is 8.

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Answer 2

Solution :

Let the natural number be "x".

According to statement :

• x + 12 = 160/x

=> x(x + 12) = 160

=> x² + 12x = 160

=> x² + 12x - 160 = 0

=> x² + 20x - 8x - 160 = 0

=> x(x + 20) - 8(x + 20) = 0

=> (x - 8) (x + 20) = 0

=> x - 8 = 0 ; x + 20 = 0

=> x = 8 ; x = - 20

As, The given number is a natural number so we will reject x = - 20.

So, The given number is 8.