Question

A rational number is such that when you multiply it with $\frac{5}{2}$ and add $\frac{2}{3}$ to the product, you get $-\frac{7}{12}$. What is the number?

• A. $-\frac{4}{3}$
• B. $-\frac{1}{2}$
• C. $\frac{4}{3}$
• D. $-\frac{5}{3}$

Answer 1

Answer: (B)

$-\frac{1}{2}$

Let the required number be $x$. Then,

$x\times \frac{5}{2}+\frac{2}{3}=-\frac{7}{12}$

$\Rightarrow \frac{5}{2}x=-\frac{7}{12}-\frac{2}{3}$ ....[Transposing $\frac{2}{3}$ to RHS]

$\Rightarrow \frac{5}{2}x=\frac{-7-8}{12}$ ....[By taking LCM on RHS]

$\Rightarrow \frac{5}{2}x=\frac{-15}{12}\Rightarrow x=\frac{-15}{12}\times \frac{2}{5}\Rightarrow x=-\frac{1}{2}$

Hence, the required number be $-\frac{1}{2}.$