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

Options

A. 7
B. -7
C. -8
D. 8

Answer

D

Explanation

Let the natural number be `x`
According to the question
`x+12=160/x`
On multiplying by `x` on both sides, we get
`implies x^(2)+12x-160=0`
`x^(2)+(20x-8x)-160=0`
`implies x^(2)+20x-8x-160=0` [by factorisation method]
`impliesx(x+20)-8(x+20)=0`
`implies (x+20)(x-8)=0`
Now `x+20=0implies x=-20` which is not possible because natural number is always greater than zero and `x-8=0impliesx=8`.
Hence, the required natural number is 8.