Question

By selling $25$ lamps shades at a price of $\mathrm{Rs}.205\frac{1}{2}$ each , Farida made a profit of $\mathrm{Rs}.137\frac{1}{2}$ . For how much did she purchase the lamp shades .

Answer 1

Step 1 : Find the selling price of $25$ lamp shades.

Selling Price of $1$ lamp shade$=\mathrm{Rs}.205\frac{1}{2}$

$=\mathrm{Rs}.\frac{411}{2}$

So, selling Price of $25$ lamp shades $=$Selling price of $1$ lamp shade $\times 25$

$$\begin{gathered} =\frac{411}{2}\times 25 \\ =\mathrm{Rs}.\frac{10,275}{25} \end{gathered}$$

Step 2 : Find the cost price of $25$ lamp shades.

Profit she gained $=\mathrm{Rs}.137\frac{1}{2}$

$=\mathrm{Rs}.\frac{275}{2}$

Since, $\text{Profit}=\text{S.P}–\text{C.P}$

$\Rightarrow \mathrm{C}.\mathrm{P}.=\mathrm{S}.\mathrm{P}.-\mathrm{Profit}$

$$\begin{gathered} \Rightarrow \mathrm{C}.\mathrm{P}=\frac{10,275}{2}-\frac{275}{2} \\ \Rightarrow \mathrm{C}.\mathrm{P}=\frac{10,275-275}{2} \\ \Rightarrow \mathrm{C}.\mathrm{P}.=\frac{10,000}{2} \\ \Rightarrow \mathrm{C}.\mathrm{P}=\mathrm{Rs}.5000 \end{gathered}$$

Hence, she purchased all the lamp shades in $\mathrm{Rs}.5000$