Question

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

Answer 1

Let the natural number = c

If the number increased by 12 = x + 12

Reciprocal of the number = 1/x

According to the problem given,

x + 12 = 160 times of reciprocal of x

x + 12 = 160/ x

x( x + 12 ) = 160

x^2 + 12x - 160 = 0

x^2 + 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.

Therefore,

Required number = x = 8

Answer 2

Hi ,

Let as assume a natural number be x

reciprocal of the number = 1/x

according to the problem given ,

x + 12 = 160 × ( 1/x )

=> x( x + 12 ) = 160

=> x² + 12x - 160 = 0

Splitting the middle term ,

=> 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.

Therefore ,

Required natural number = x = 8

I hope this helps you.

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