Question

A number is added to $2\frac{1}{2}$ and the sum is multiplied by $4\frac{1}{2}$. Then 3 is added to the product and the sum is divided by $1\frac{1}{5}$ which gives the quotient as 25. What is the number?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let the number be x. Then,

$\frac{4\frac{1}{2}\left(x+2\frac{1}{2}\right)+3}{1\frac{1}{5}}=25\Rightarrow \frac{\frac{9}{2}\left(x+\frac{5}{2}\right)+3}{\frac{6}{5}}=25$

$\Rightarrow \frac{9x}{2}+\frac{45}{4}+3=25\times \frac{6}{5}=30\Rightarrow \frac{9x}{2}=30-\frac{57}{4}\Rightarrow \frac{9x}{2}=\frac{63}{4}$

$\Rightarrow x=\left(\frac{63}{4}\times \frac{2}{9}\right)=\frac{7}{2}=3\frac{1}{2}$