# 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+45-80 = 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+15-300/100 = 35-3 = 32%
Marked price * 68/100 = 136
Marked Price = 136 * 100/68 = Rs.200

Two 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.

24-Cost Price/Cost price = Cost price/100
(Cost Price)^2 +100 * Cost price – 2400 = 0
(Cost price +120) * (Cost price-20) = 0
Cost price = -120 or 20
Since price cannot take negative value , Cost price = Rs.20

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