The difference between tow selling prices of a shirt at profits of 4% and 5% is Rs 6. Find the two selling prices of the shirt
$$\textbf{Step 1: Find the cost price of the shirt.}$$
$$\text{Given, }$$
$$\text{Selling price with 5% profit}-\text{Selling price with 4% profit}=Rs. 6$$
$$\text{Let, x be the cost price of the shirt}$$
$$\text{Now, }$$
$$x\times \left(1+\dfrac{5}{100}\right)-x\times\left(1+\dfrac{4}{100}\right)=6$$
$$x\times \left(1+\dfrac{5}{100}-1-\dfrac{4}{100}\right)=6$$
$$x\times \left(\dfrac{1}{100}\right)=6$$
$$\text{Cost price of the shirt}=x=Rs. 600$$
$$\textbf{Step 2: Find the selling price of shirt with 4% and 5% profits.}$$
$$\text{Selling price with 4% profit}=600\times\left(1+\dfrac{4}{100}\right)$$
$$=6\times104$$
$$=Rs. 624$$
$$\text{Selling price with 5% profit}=600\times\left(1+\dfrac{5}{100}\right)$$
$$=6\times105$$
$$=Rs. 630$$
$$\textbf{Hence, selling price of shirt with 4% and 5% respectively are Rs. 624 and Rs. 630. }$$