Profit & Loss

Concepts:
%Profit = (Profit/Cost Price)*100 = (Selling Price – Cost price)*100/Cost Price
%Loss = (Loss/Cost Price)*100 = (Cost Price – Selling Price)*100/Cost price
%Discount = Discount*100/Marked Price
Selling Price = Marked Price – Discount
If two items are sold, each at Rs.x one at a gain of P% and the other at a loss of P%, there is an overall loss given by (P^2/100) %. The absolute value of the loss is given by (2P^2x/ (100^2 – P^2)).
If cost price of two items is same and %Loss and %Gain on the two items are equal, then net loss or net profit is zero.
If (x+y) articles are sold at cost price of x articles then the percentage discount = Y*100/(x+Y).
In case of successive discounts a% and b% the effective discount is (a+b(ab/100)) %
By using false weight , If a substance is sold at cost price, the overall gain % is given by (100+Gain % )/100 = True scale Weight/False scale Weight.
Questions
A boy buys eggs at 9 for Rs.16 and sells them at 11 for Rs.20.What is his gain or loss percentage?
Let number of eggs bought and sold be lcm of 11 and 9 which is 99
Cost price of 99 eggs = 99 * 16/9 = Rs.176
Selling price of 99 eggs = 99 * 20/11 = Rs. 180
Profit = Rs.4
Profit % = 4 * 100/176 = 2.273%A dishonest dealer professes to sell his goods at cost price, but uses a weight of 960gm for the kg weight. Find his gain percent.
100+Gain%/100 = True scale weight/False scale weight
Gain % = (100*1000/960) – 100 = 104.166 100 = 4.16%A man purchases a certain number of oranges at 25 a rupee and same number at 20 a rupee. He mixes them together and sells them at 45 for two rupees. How much percent does he gain or lose in the transaction?
LCM (25,20,45) = 900
Cost price of 900 orange which is purchased 25 at a rupee = 900/25 = Rs.36
Cost price of 900 orange which is purchased at 20 a rupee = 900/20 = Rs.45
Selling price of 1800 oranges which is sold at 45 for two rupees = 1800 * 2/45 = Rs.80
Loss = 36+4580 = Rs.1
Loss % = 100/81 % = 1.23%The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percent.
Let cost price of one article be Rs.1.
Cost price of 10 articles Rs.10
Selling price of 9 articles Rs.10
Selling price of 10 articles = 10 +10/9 = 100/9
Profit = 100/9  10 = 11.11 – 10 =Rs.1.11
Profit % = 1.11*100 / 10 = 11.11%A trader allows two successive discounts of 20% and 15%. If he gets Rs.136 for an article, find its marked price.
Effective discount = (a+b(ab/100)) %
= 20+15300/100 = 353 = 32%
Marked price * 68/100 = 136
Marked Price = 136 * 100/68 = Rs.200Two goods are sold at the same price one at a loss of 15% and other at a profit of 15%.Find the overall profit/loss.
Overall loss = (P^2/100) % = 225/100 = 2.25%
Selling an article for Rs.24, the profit percentage is equal to the cost price In rupees. Find the cost price of article.
24Cost Price/Cost price = Cost price/100
(Cost Price)^2 +100 * Cost price – 2400 = 0
(Cost price +120) * (Cost price20) = 0
Cost price = 120 or 20
Since price cannot take negative value , Cost price = Rs.20