Profit and Loss
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- Cost Price – The amount paid for a product to purchase it is called it's cost price.
- Selling Price – The amount at which the product is sold is called it's selling price. It is also called as sale price.
- Profit – If selling price of any item is more than the cost price of the item then there is a profit on the selling the item.
- Loss – If selling price of any item is less than the cost price of the item then there is a loss on the selling the item.
- $$Profit\% = \left( {{{Gain \times 100} \over {CP}}} \right)$$
- $$Loss\% = \left( {{{Loss \times 100} \over {CP}}} \right)$$
- $$CP = \left[ {{{100} \over {\left( {100 + Gain\% } \right)}} \times SP} \right]$$
- $$CP = \left[ {{{100} \over {\left( {100 – Loss\% } \right)}} \times SP} \right]$$
$$Profit = Selling\ Price – Cost\ Price$$
$$Loss = Cost\ Price – Selling\ Price$$
- $$SP = \left[ {{{\left( {100 + Gain\% } \right)} \over {100}} \times CP} \right]$$
- $$SP = \left[ {{{\left( {100 – Loss\% } \right)} \over {100}} \times CP} \right]$$
- Marked Price (MP): Marked Price is labelled by shopkeepers to offer a discount to the customers in such a way that.
- Discount – Sometimes shopkeeper gives you some rebate on items for selling to their customers. This rebate is known as discount.
- $$Discount = Marked\ Price – Selling\ Price$$
- When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss:$$\ Loss\% = {\left( {{{Common\,Loss\,and\,Gain\,\% } \over {10}}} \right)^2}$$
- When there are two successful profit's say m% and n%, then the net percentage profit is equal to:$$\ \left( {{{m + n + mn} \over {100}}} \right)$$
- When the profit is m% and loss is n%, then the net % profit or loss will be:$$\ \left( {{{m – n – mn} \over {100}}} \right)$$
- If a product is sold at m% profit and then again sold at n% profit then the actual cost price of the product will be:$$\ CP = \left[ {100 \times {{100 \times P} \over {(100 + m)(100 + n)}}} \right]$$
- If a product is sold at m% loss and then again sold at n% loss then the actual cost price of the product will be:$$\ CP = \left[ {100 \times {{100 \times P} \over {(100 – m)(100 – n)}}} \right]$$
1 A machine is sold at a profit of 10%. Had it been sold for ₹ 80 less, there would have been a loss of 10%. Find the cost price of the machine is:
2 By selling 25 mangos a trader gains the selling price of 5 mangos. The gain percent of the trader in % is:
3 A shopkeeper sold some coconuts at ₹35 per coconut and earned a profit of 40%. At what price each coconut should have been sold so that 60% profit was earned?
4 On selling 50 Oranges, a merchant made a loss equal to selling price of 25 Oranges. Find his loss percentage:
5 If the profit on selling an Pizza for ₹ 579 is the same as the loss on selling it for ₹ 337, then find the profit percent if it's selling price is ₹ 687:
6 An Necklace is sold at a profit of 50%. If the cost price is doubled and the selling price is halved, then what will be the new profit or loss percentage?
7 A dealer sold a Cement mixer at a loss of 2.5%. Had he sold it for ₹100 more, he would have gained 7.5%. In order to gain 12.5%, he should sell it for?
8 A shopkeeper sells an Umbrella at a profit of 20%. If he reduces the price of the Umbrella by ₹ 700, he incurs a loss of 15%. What is the cost price of the Umbrella?
