Question

The sum of thrice a number and twice its reciprocal is 97/4. What is the number?

A) 9 B) 10 C) 8 D) 7

Answer 1

$\huge\mathfb{Solution :-}$

Let the number be :- x

Therefore according to question ,

3x + 2 ( 1 / x ) = 97 / 4

➡ 3x + 2 / x = 97 / 4

➡ 3x = 97 / 4 - 2 / x

➡ 3x = 97 x - 8 / 4x

➡ 12x² = 97x - 8

➡ 12x² - 97x + 8 = 0

➡ 12x² - ( 96 + 1 )x + 8 = 0

➡ 12x² - 96x - x + 8 = 0

➡ 12x ( x - 8 ) - 1 ( x - 8 ) = 0

➡ ( 12x - 1 ) ( x - 8 ) = 0

12x - 1 = 0

➡ x = 1 / 12

x - 8 = 0

➡ x = 8

Now in the option we have 8 so the value of x we will take 8 rather than 1 / 12

Therefore, option c) that is 8 is the correct one