百分比变化是指商品计量基础的变化概念，即商品的净值增加或减少的数量。当商品价值发生变化(即增加或减少某个数值)时，发生百分比变化。可能出现三种情况：
增长百分比
当新值大于旧值时，在这种情况下，会注意到数字值的增加。
Increase = New value – old value
Percentage Increase is given by,
Percentage Increase = Increase × 100
Old value
减少百分比
当旧值大于新值时，在这种情况下，数字值会减小。
Decrease = Original value – New value
Percentage Decease = Decrease × 100
Original value
没有变化
当旧值等于新值时，在这种情况下，既没有增加也没有减少，并且净百分比变化= 0％。
百分比变化的样本问题
以下示例说明了百分比更改的概念：
问题1：Ram最初以10卢比的价格带了一支铅笔。后来，价格定为₹5。告诉它是增加还是减少，以及增加了多少百分比。
解决方案：
Original/Old value = ₹10
New value = ₹5
Since, old value > new value, there is a decrease in value and therefore, percentage decrease is given by,
Old value – New value × 100
Old value
⇒ (10 – 5) × 100
10
⇒ 1 × 100 = 50%
2
Therefore, there is a net percentage decrease of 50%.
问题2：某商品的新价值为₹20，涨幅为-40％。查找商品的原始价值。
解决方案：
Now, new value = ₹20
Percentage increase = -40%, which means there is a net decrease
Let original value = x
Percentage decrease = x – 20
x
⇒ 40 = x – 20 × 100
x
⇒ 40x = (x – 20)×100
⇒ 2000 = 60x
⇒ x = 2000
60
⇒ 33.333
≈ 33.34
Therefore, original price was ₹33.34.
问题3： 2009年的年降雨量为300平方厘米。然而，在2010年，降雨量很大，达到600平方厘米。降雨量增加了多少?
解决方案：
Here,
2009 Annual rainfall = 300 sq.cm
2010 Annual rainfall = 600 sq.cm
Here we can easily see there is increase in the annual rainfall
So,
Percentage increase = 2010 Annual rainfall – 2009 Annual rainfall × 100
2009 Annual rainfall
⇒ 600 sq.cm – 300 sq.cm × 100
300 sq.cm
⇒ 300 sq.cm × 100
300 sq.cm
⇒ 100%
Therefore, the Annual rainfall is increased by 100%.
问题4：正方形的边最初是4厘米。进行修改后，将其调整为3厘米。正方形的面积变化了多少?
解决方案：
Here,
Initial area of square = Side × Side
= 4 cm × 4 cm
= 16 sq.cm
Amendment area of square = 3 cm × 3 cm
= 9 sq.cm
Here we can see the area has been decreased.
So,
Percentage Decreased = Initial area – Amendment area × 100
Initial area
⇒ 16 – 9 × 100
16
⇒ 7 × 100
16
⇒ 43.75%
Therefore, the area of square after amendment is decreased by 43.75%.
折扣如何运作?
在标价上提供折扣，从而降低了客户的商品售价。
Discount(D) = Marked price(M.P.) – Selling price(S.P.)
Also,
Discount percentage = Discount × 100
Marked price
折扣样本问题
问题1：找到折扣率和折扣。一个玩具的MP为₹1000，打折后以£800的价格卖给了Shyam。找出玩具给Shyam节省了多少钱。
解决方案：
Now, M.P = ₹1000
S.P = ₹800
Discount = M.P -S.P
= ₹200
Also, discount percentage = Discount×100
M.P
= 200 × 100
1000
= 20%
问题2：Sita在Ramlal先生提供15％的折扣后，以₹500的价格从Ramlal先生那里购买了一件商品。这篇文章最初对拉姆拉尔先生花费了多少?
解决方案：
Now, Selling Price, S.P = ₹500
Discount percentage = 15%
Let Market Price = x
Now, Discount percentage = x – 500 ×100
x
15 = (x – 500) ×100
x
15x = (x – 500)×100
15x = 100x – 50000
85x = 50000
x = 588.23
Therefore, the article costed Mr Ramlal ₹588.23.
问题3：一件夹克的标价是2500卢比。讨价还价后， Mallika则以₹1750的价格购得。 Mallika以什么折扣得到了夹克?
解决方案：
Here,
Marked Price, M.P. = ₹2500
Selling Price, S.P. = ₹1750
Now, Discount Percentage = ₹2500 – ₹1750 × 100
2500
⇒ ₹750 × 100
₹2500
⇒ 30%
Therefore, Mallika brought jacket at 30% discount.
问题4：一位店主以￥ 15500的价格售出了一台冰箱。他给了标价15％的折扣，但仍获得了8％的折扣。找到标价的冰箱了吗?
解决方案：
Cost Price of the refrigerator = ₹15500,
Gain% = 8%.
Therefore, Selling Price = [{(100 + gain%)/100} × CP]
= ₹ [{(100 + 8)/100} × 15500]
= ₹ [(108/100) × 15500]
= ₹ 16740.
Let the Marked Price be ₹ ‘x’.
Then, the discount = 15% of ₹x
= ₹ {x × (15/100)}
= ₹ 3x/20
Therefore, SP = (Marked Price) – (Discount)
= ₹(x – 3x )
20
= ₹ 17x
20
But, the SP = ₹ 16740.
Therefore, 17x = ₹16740
20
⇒ x = (16740 × 20 )
17
⇒ x = ₹19695.
Hence, the marked price of the refrigerator is ₹19695.