# Sale Price, Gross Margin determination – Simple Trick

I am going to share with you one trick which one great teacher, Mr S.K. Jha taught me. Simple arithmetical problems of

Finding out selling price, when cost price and margin (percentage of profit on Sale) are given. Or,

Finding out cost price when Sale price is given and percentage of profit on cost is given.

Finding out the mark-up when cost price and Sale price are given.

We all have seen occurrence of such problems in our academic life and day-to-day life. All the time we need a paper – pen or a calculator. But now with the process given below I believe we can solve any such problem in our mind.

To keep it simple, I will use the same language used by **Mr. Jha (Sir)** to explain me when I was kid.

**Relation between Cost Price and Sale Price**

If profit = ½ of cost = 1/3 of sales

If profit = 1/3 of cost = 1/4 of sales

If profit = 1/4 of cost = 1/5 of sales

If profit = 1/5 of cost = 1/6 of sales

–

–

If profit = 1/49 of cost = 1/50 of sales

and so on

**Generalization of above method**

1/x of cost = 1/(x+1) of sales.

i.e. adding 1 to the denominator if you are moving from cost to sales .

subtracting 1 from the denominator if you are moving from sales to cost

Sir asked me, “isn’t it very simple. You just have to convert any percentage into fraction and apply the above method.”

I was amazed by the simplicity of the concept, but a question cropped up in my mind. What if the numerator is not equal to 1?

He had the answer ready, “You can convert any numerator into 1. Say for example you need to earn 60% margin on an article worth (costing) Rs. 40

Now, Profit = **60 % of sales** = 60/100 of sales = 3/5 of sales = 1/(5/3) of sales

Now, Profit = 1/(5/3) of sales = 1/(5/3 – 1) of cost = 1/(2/3) of sales = **3/2 of cost**

Now since, cost price = 40, Profit = 40 * 3/2 = 60 , sale price = 40+60 = 100

**Alternative method,**

Add the numerator to the denominator, when moving from cost to sales.

150 % of cost = 3/2 of cost = 3/(2+3) of sales = 3/5 of sales = **60 % of sales**

Deduct the numerator from the denominator, when moving from sales to cost.

For example take the above case, 60/100 of sales = 60/40 of cost = **3/2 of cost**

If you want to share such simple tricks with other via QuickerMaths.com, send them across to me @ vineetpatawari@gmail.com

Thanx a lot vineeth it held me a lot I had a confusion always with this prblm how much on cost thn sales……..thanx for sharing ur knowledge

what if I some one sold goods of 27000 rupees. with the 118.75% profit what is the purchasing amount of sale.

What will happen if I have 125% profit on sales? What is the profit on cost then? I guess this trick doesn’t work where profit on sales exceeds 100%

Profit % on sales can’t be greater than 100. So the trick will apply in all cases!

Please tell what aur how to do if profit percentage is on selling price. Example if I say profit percentage is 10% then we say that CP would be 100 and selling price would be 110. But what if I say profit percentage is on selling price then profit percentage is 10% what about cp and sp

well…i already knew this trick my friend told me a year ago…jst refreshed my memory,,…very useful trick,,,100% full proof…

I have buying price,selling price and profit margin.I need to calculate my profit in percentage.I created two formulas for that.But confused that which is right.

(1) profit x 100 /selling price

(2) profit x 100 /buying price.

Which is right?

profit margin has selling price as denominator.

profit percentage in mathematics has cost or buying price has denominator.

In your case, option (2) is correct.

how is that poss?

if u want to earn 60% profit on Rs.40 and selling it for 100. Then profit % will be (100-40)/40 x 100=150% not 60%

check ur question again

very complicated language

Yea!!! Really GR8…

Terrific work! This is the type of information that should be shared around the web. Shame on the search engines for not positioning this post higher!

@ Anupma Gupta – He is indeed a great teacher. Thanks for the appreciation. It’s very encouraging.

your teacher Mr Jha must be too good. this is an awesome trick.hats off !!!