Question

Find $y$, if $\frac{1}{2}(3y+1)-\frac{1}{3}(5y+2)=y-1$.

• A. $5$
• B. $7$
• C. $\frac{5}{7}$
• D. $\frac{7}{5}$

Answer 1

Answer: (C)

$\frac{5}{7}$

Given, $\frac{1}{2}(3y+1)-\frac{1}{3}(5y+2)=y-1$

$\Rightarrow$ $\frac{3(3y+1)-2(5y+2)}{6}=y-1$ …[Cross-multiplying the denominators on the LHS]

$\Rightarrow$ $9y+3-10y-4=6y-6$ …[Cross-multiplying the denominator]

$\Rightarrow$ $-y-1=6y-6$.

Transposing $x$ terms to one side, we get,
$\Rightarrow$ $7y=5$

$\Rightarrow$ $y=\frac{5}{7}$.

Hence, option $C$ is correct.