Question

Divide$4500$ into two parts such that $5\%$of the first part is equal to$10\%$ of the second part.

Answer 1

Let, the first part and second part be $x$ and $y$ respectively.

Step 1: Write $y$ in terms of $x$

$5\%$of the first part $=\frac{5x}{100}$

$10\%$of the second part $=\frac{10y}{100}$

According to the question, $5\%$of the first part is equal to the $10\%$ of the second part.

$\Rightarrow$$\frac{5x}{100}=$ $\frac{10y}{100}$

$\Rightarrow$ $5x=10y$

$\Rightarrow$ $\frac{5x}{10}=y$

$\Rightarrow$ $\frac{x}{2}=y$

$\Rightarrow$ $y=\frac{x}{2}$

Step 2: Find the value of $x$ and $y$

It is given that the sum of both the parts is $4500$.

$\Rightarrow$ $x+y=4500$

$\Rightarrow$ $x+\frac{x}{2}=4500$

$\Rightarrow$$\frac{2x+x}{2}=4500$

$\Rightarrow$ $\frac{3x}{2}=4500$

$\Rightarrow$ $3x=4500\times 2$

$\Rightarrow$ $x=3000$

If $x=3000$, $y=\frac{3000}{2}$ ( as $y=\frac{x}{2}$)

$\Rightarrow$ $y=1500$

Hence, $4500$ can be divided into $3000$ and $1500$ to satisfy the given conditions.