Question

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

Answer 1

This is your answer buddy..!

Answer 2

Answer

• Number = 8

Given

• A natural number, when increased by 12 equals to 160 times its reciprocal

To Find

• The number

Solution

Let the number be " x "

When number is increased by 12 = " x + 12 "

Reciprocal of the number = " ¹/ₓ "

A/c , " A natural number, when increased by 12,equal 160 times its reciprocal "

$\implies \tt ( x+12)=160 \times \dfrac{1}{x}\\\\\implies \tt x+12=\dfrac{160}{x}\\\\\implies \tt x(x+12)=160\\\\\implies \tt x^2+12x=160\\\\\implies \tt x^2+12x-160=0\\\\\implies \tt x^2-8x+20x-160=0\\\\\implies \tt x(x-8)+20(x-8)=0\\\\\implies \tt (x-8)(x+20)=0\\\\\implies \tt x=8\;\; \& \;\;x=-20\\\\\implies \tt x=8$

Since , x can't be -ve , ∵  it is a natural number

Verification

$\tt x+12=\dfrac{160}{x}\\\\\implies \tt 8+12=\dfrac{160}{8}\\\\\implies \tt 20=20$

Hence verified