仅当售价>成本价时，一个人才能获得利润。此外，当售价<成本价时，人会产生损失。因此，让我们详细了解每个术语。
售价(SP)
定义：店主向客户出售商品的价格称为销售价格(SP)。
公式：在已知(利润/成本)％的情况下计算售价(SP)：
Selling Price (S.P) = { [ ( 100 + Profit ) / 100 ] * C.P }
Selling Price (S.P) = { [ ( 100 – Loss) / 100 ] * C.P }
成本价(CP)
定义：店主从卖方购买商品的价格称为成本价格(CP)。
公式：在已知(利润/成本)％的情况下，计算成本价格(CP)：
Cost Price (C.P) = { [ 100 / (100 + Gain ) ] * S.P }
Cost Price (C.P) = { [ 100 / (100 – Loss ) ] * S.P }
利润
定义：如果某物品的销售金额大于该特定物品的购买金额，则称为利润。
公式：
Profit = Selling Price(S.P) – Cost Price(C.P)
失利
定义：如果某物品的销售金额少于该特定物品的购买金额，则称为损失。
公式：
Loss = Cost Price(C.P) – Selling Price(S.P)
利润百分比
公式：
Profit % = [ ( Profit * 100 ) / C.P ]
损失百分比
公式：
Loss % = [ ( Loss * 100 ) / C.P ]
给出成本价(CP)和获利百分比或亏损％时的售价(SP)
公式：
S.P when C.P and Gain % are given:
= [ (100 + Gain % ) / 100 * C.P ]
S.P when C.P and Loss% are given:
= [ (100 – Loss% ) / 100 * C.P ]
给出售价(SP)时的成本价格(CP)和收益％或亏损％
公式：
C.P when S.P and Gain % are given:
= [ 100 / ( 100 + Gain % )* S.P ]
C.P when S.P and Loss% are given:
= [ 100 / ( 100 – Loss % )* S.P ]
例子
例子1.一个学生以600卢比的价格买了一本书，以700卢比的价格卖了一本书。
解决方案：
Given, Cost Price of book = ₹ 600
Selling Price of book = ₹ 700
By using the gain formula,
Gain = Selling Price – Cost Price
= 700 – 600
= ₹ 100
By using the gain% formula,
Gain% = (gain/cost price) * 100
= (100/600) * 100
= 100/6
= 16.66%
示例2. Sonia以450000卢比的价格购买了一辆汽车。她使用了三个月，然后以435000卢比的价格出售了。
解决方案：
Given, C.P = ₹ 450000 and S.P = ₹ 435000
∴ Loss = C.P – S.P
= ₹ ( 450000 – 435000 )
= ₹ 15000
Loss % = [ ( Loss / C.P ) * 100 ] %
= [ ( 15000 / 450000 ) * 100 ] %
= 10/3 %
So, the loss percent = 10/3 %
例子3. Sneha花了3500卢比买了一辆自行车，花了1000卢比修理自行车。她以40％的收益出售了它。她卖了多少钱的自行车?
解决方案：
Total cost price of the bicycle = price paid to purchase it + Repair charges
C.P = ₹ (3500 + 1000) = ₹ 4500
S.P = [ (100 + Gain % ) / 100 * C.P ]
= [ ( 100 + 40 ) /100 * ₹ 4500 ]
= ₹ 140/100 * 4500
= ₹ 6300
So, Sneha sold the bicycle for ₹ 6300
示例4.一位商人以₹12880的价格出售iPod损失了8％。为了获得8％，他应该以什么价格卖出?
解决方案：
S.P of the iPod = ₹12880 , Loss % = 8%
C.P of the iPod = [ 100 / ( 100 – Loss % ) * S.P ]
= [ ( 100 / 100 – 8 ) * ₹12880 ]
= ₹ 100 / 92 * 12880 = ₹ 14000
Now, C.P = ₹14000, Gain % = 8%
S.P of the iPod = [ (100 + Gain % ) / 100 * C.P ]
= [ ( 100 + 8 ) / 100 * ₹14000
= ₹ ( 108 / 100 ) * 14000
= ₹15120
So, he should sell the iPod at ₹15120 to gain a profit of 8%.
例子5 。一个人购买了价值4500卢比的商品，并以10％的损失出售了1/3的商品。他应以多少百分比的价格出售剩余的商品，以便在整个交易中获得20％的利润?
解决方案：
C.P of goods = ₹ 4500, Gain = 20%
S.P of goods = [ (100 + Gain % ) / 100 * C.P ]
= [ ( 100 + 20 ) / 100 * ₹ 4500
= ₹ 120/100 * 4500
= ₹ 5400
C.P of 1/3 of the goods = ₹ (1/3 * 4500 ) = ₹ 1500
∴ S.P of 1/3 of the goods at a loss of 10%
= [ (100 – Loss% ) / 100 * C.P ]
= [ ( 100 – 10 ) /100 * ₹ 1500 ]
= ₹ 90/100 * 1500 = ₹ 1350
∴ S.P of the remaining goods = S.P of all the goods – S.P of 1/3 of the goods
= ₹ 5400 – ₹ 1350 = ₹ 4050
∴ C.P of the remaining goods = C.P of all the goods – C.P of 1/3 of the goods
= ₹ 4500 – ₹ 1500 = ₹ 3000
Gain = S.P – C.P
= ₹ 4050 – ₹ 3000 = ₹ 1050
Gain % = ( Gain /C.P ) * 100% = ( 1050/3000 ) * 100% = 35%
So, The man should sell the remaining goods at a gain of 35%.