Question

Solve : $\frac{1}{3x}+\frac{1}{4x}+\frac{1}{2x}+\frac{1}{6x}=5$

• A. $x=\frac{1}{2}$
• B. $x=\frac{1}{8}$
• C. $x=\frac{4}{1}$
• D. $x=\frac{1}{4}$

Answer 1

The correct option is D

$x=\frac{1}{4}$

Multiplying the equation by $12x$ (the L.C.M. of the denominator) we get,

$\Rightarrow (\frac{1}{3x}+\frac{1}{4x}+\frac{1}{2x}+\frac{1}{6x})\times 12x=5\times 12x$

$\Rightarrow \frac{1}{3x}\times 12x+\frac{1}{4x}\times 12x+\frac{1}{2x}\times 12x+\frac{1}{6x}\times 12x=5\times 12x$

$\Rightarrow 4+3+6+2=60x$

$\Rightarrow 15=60x$

$\Rightarrow x=\frac{15}{60}=\frac{1}{4}$

$\therefore x=\frac{1}{4}$