Question

When $2\frac{1}{2}$ is added to a number and the sum is multiplied by $4\frac{1}{2}$ and then $3$ is added to the product and then the sum is divided by $1\frac{1}{5}$, the quotient becomes $25$. What is that number

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

Answer 1

The correct option is B $3\frac{1}{2}$

Let the required number be $x$. We will write each step separately.

In the first step, we add $2\frac{1}{2}=\frac{5}{2}$ to get $x+\frac{5}{2}$.

In the second step, we multiply the result by $4\frac{1}{2}=\frac{9}{2}$ to get $\frac{9x}{2}+\frac{45}{4}$.

In the third step, we add 3 to the result to get $\frac{9x}{2}+\frac{57}{4}$.

In the last step, we divide by $1\frac{1}{5}=\frac{6}{5}$ to get $\frac{45x}{12}+\frac{285}{24}$. It is given to us that this number is equal to 25.

So we have to solve for $x$ in the equation $\frac{45x}{12}+\frac{285}{24}=25$.

$⟹90x+285=600$

$⟹90x=315$

$⟹x=\frac{7}{2}$

So, $x=3\frac{1}{2}$.