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
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
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