Reverse Calculate Selling Price(without Markup GST), when you have Buying Price(with GST) and Selling Price(with Markup GST)

Consider this scenario:

1. buying_price + buying_gst = buying_total
and
2. selling_price + mark_up_gst = selling_total

You have buying_total , selling_total , and gst_percentage(on Mark up). How would you derive a formula for selling_price? Here is the derivation: (Note: '*' means multiply, '/' means divide)

Step 1:
selling_total = selling_price + mark_up_gst

Step 2:
selling_total = selling_price + (mark_up_amount*gst_percent/100)

Step 3:
selling_total = selling_price + [(selling_price-buying_total)*gst_percent/100]

Step 4:
(100*selling_total) = (100*selling_price) + [(selling_price-buying_total)*gst_percent]

Step 5:
(100*selling_total) = (100*selling_price) + (selling_price*gst_percent)-(buying_total*gst_percent)

Step 6:
(100*selling_total) = selling_price(100+gst_percent) - (buying_total*gst_percent)

Step 7:
(100*selling_total) + (buying_total*gst_percent) = selling_price(100+gst_percent)

Step 8:
selling_price(100+gst_percent) = (100*selling_total) + (buying_total*gst_percent)

Step 9:
selling_price = [(100*selling_total) + (buying_total*gst_percent)]/(100+gst_percent)

Step 10:
selling_price = [(100*selling_total) + (buying_total*gst_percent)]/(100+gst_percent)


So here we have the final formula we wanted to have:

selling_price = [(100*selling_total) + (buying_total*gst_percent)]/(100+gst_percent)